The wiener index is a distancebased graph invariant, used as one of the structure descriptors for predicting physicochemical properties of organic compounds often those signi. Gives the probability that any two individuals drawn at random from an infinitely large community belong to different species iii. Wiener indices of catacondensed cyclic graph with its characteristic graph and give the wiener number for two cycles sharing maximum and minimum number of edges. Since then it has become one of the most frequently used topological indices in chemistry, as molecules are usually modelled as undirected graphs, especially trees. Based on its success, many other topological indexes of chemical graphs, based on information in the distance matrix of the graph, have been developed subsequently to wiener s work. This algorithm improves and simplifies a nice recursive algorithm of canfield, robinson and rouvray 5. The hyper wiener index of acyclic graphs was introduced by milan randi c in 1993 see 2. Wiener index in this section we compute the wiener index of cluster of two graphs. Wiener index of some cycle related graphs using matlab. With signature clarity and humor, eric weiner picks up where the good place left off. We suggest an explanation for this dual use of terms and in so doing we offer a tribute to the late claude shannon who passed away on 24 february 2001. A modification of the weiner index which properly takes into account the symmetry of a graph is proposed.
The plots are located in two national parks, and are. The wiener index can also be expressed in terms ofthe mti for ncyclesde. Molecular graphs and the inverse wiener index problem. The list of the six most exciting books of the season, is curated by malcolm gladwell, adam grant, susan cain and dan pink. We characterize eulerian graphs with a fixed number of vertices with smallest and greatest wie. A new method to find the wiener index of hypergraphs. If g is a connected graph, then the distance between two edges is, by definition, the distance between the corresponding vertices of the line graph of g. On the wiener indices of trees ordering by diametergrowing. Search the worlds most comprehensive index of fulltext books. Where ni number of individuals or amount of each species i. The hyperwiener index of unicyclic graph with given diameter. The edge wiener index we of g is then equal to the sum of distances between all pairs of edges of g. The wiener related indices of some graph operations. Since calculating the wiener index of a graph can be computationally expensive, we give some cheaply computable lower and upper bounds for the wiener index given certain graph properties in chapter 3.
Wiener index is the oldest and one among the most investigated topo. The explicit formulae for the modified wiener index of path, cycle, complete bipartite, cube and lattice graphs are derived and compared with their standard wiener index. Similar to the symbol wg for the wiener index, the hyper wiener index is traditionally denoted by wwg. The wiener index is analyzed for random recursive trees and random binary search trees in the uniform probabilistic models. Acta 77 12 6164 2004 55 60 65 70 75 80 85 80 100 120 140 160 180 200 220 ww w 55 60 65 70 75 80 85 160 180 200 220 240 260 www w figure 3. The shannon index is a popular diversity index in ecology taking into account the number of species as well as the evenness of species how close in numbers each species in an environment are. Statistics shannon wiener diversity index tutorialspoint. Wiener index of hexagonal systems university of ljubljana. Differences between detour and wiener indices the australasian. Eric weiner author, speaker, philosophical traveler. Let g be a molecular graph and vv v12,, n be its vertices. This short article about sports can be made longer.
The wiener index is one of the most studied topological indices, both from a theoretical point of view and applications. A relation between dindex and wiener index for rregular graphs. On the occasion of the fiftieth anniversary of the wiener index, three special journal issues were published. Volkmann, wiener index versus maximum degree in trees, discrete appl. Note on the hyper wiener index ivan gutman, boris furtulaand jasminabeli faculty of science, university of kragujevac, p. The word wiener, often misspelled as weiner, entered english around 186570, shortened from the german phrase wiener wurst, which roughly translates to vienna sausage. Apr 07, 2021 the wiener index is not very discriminant.
It was introduced in 1947 as a tool for predicting various physicochemical properties, initially applied on small, simple, and acyclic organic molecules 22 19 20. On the monday, following the third friday, the index value of the atx dvp is reset to zero. Wiener index of uniform hypergraphs induced by trees pisrt. Introductionthe wiener index wg is a distancebased topological invariant, it much used in the study of the structureproperty and the structureactivity relationships of several classes of biochemically interesting compounds introduced by harold wiener in 1947 for predicting boiling points. Wiener defined wiener index w g 3 and 8 as the sum of smallest distance between all vertices of the graph g w g, i j i j d v v the wiener index w g of a graph g is defined as the sum of the half of the distances between every pair of vertices of g. Compound indices, including variations of both the shannonwiener index and simpsons index, are assumed to intelligibly integrate species. Two vertices of lg are adjacent if and only if their corresponding edges in g share a common endvertex. It appears that for majority of chemical applications, the study of wiener index is restricted to acyclic molecular graphs although mathematical studies are reported for hexagonal systems also see dgkv02.
Wiener index is the oldest topological descriptor that found diverse applications in theoretical chemistry 21. Pdf the extremal values of the wiener index of a tree with. Abstractthe wiener index of a connected graph is defined as the sum of distances between all pairs of vertices in the graph. In 1971, hosoya was the first person who introduced the relationship between wiener index and the distances in molecular graph. Computation of topological indices of some special graphs. Pdf the edgewiener index of a graph semantic scholar. We found that finite steps of diametergrowing transformation relative to vertices can not always enable the wiener index of a tree to increase sharply. Yang presented a sufficient condition in terms of the wiener index for a graph to be traceable. The wiener index is analysed for random recursive trees and random binary search trees in uniform probabilistic models. The wiener index w is the sum of distances between all pairs of vertices of a connected graph.
Pdf wiener index of directed and weighted graphs by matlab. The wiener index is a topological index of a molecular graph, defined as the sum of distances between all pairs of its vertices. In a rare philosophy book thats a delight to read, he illuminates what deep thinkers through history have. Wang in 28 gave a mistaken result on the maximum wiener index of trees with given degree sequence. It is the oldest topological index related to molecular branching. Correlation between the wiener index w, the hyper wiener index ww and the new hyper wiener index www for isomeric octanes, cf. Jul 24, 1996 a novel unsymmetric square matrix, cju, is proposed for calculating both wiener,1 w, and hyper wiener,2 ww, numbers. The wiener index is named after harry wiener, who introduced it in 1947. The linear chain lh with h hexagons is the catacondensed system without kinks. The detour index, in contrast to the wiener index that considers the length of the shortest path.
Shannon wiener s index all species must be represented relatively easy to calculate sensitive to changes in rare species diversity and productivity ch. In this paper, we consider relationships between hypertrees and trees. The wiener index \wg\ of a graph \g\ is defined as the sum of distances between its vertices. There is some debate about whether the sausages were invented in vienna, austria, or in. In this paper, we found a general formula that links the wiener index with dindex of a regular graph g. In the seminal paper 21, the wiener index is calculated but. Kragujevacjournalof mathematics volume37 20, pages 1294.
The wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate a chemical compounds molecular graph with experimentally gathered data regarding the compounds characteristics. Kragujevacjournalof mathematics volume37 20, pages. Introduction wiener index is a wellknown graph distance invariant introduced by harold wiener 50 years ago11. The wiener index of a graph g is equal to the sum of distances between all pairs of vertices of g, it is known that the wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. This matrix is constructed by using the principle of single endpoint characterization of paths. The wiener index of a tree the main result of this section is an algorithm for computing wt for an arbitrary tree t. Jun 01, 2012 the wiener index is one of the most studied topological indices, both from a theoretical point of view and applications. We characterize graphs with the maximum wiener index among all graphs of order. On some occasions it is called the shannon wiener index and on other occasions it is called the shannonweaver index. This book explores some combinatorial and graph theoretic. The wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Of the numerous results on the wiener index of line graphs are we mention here1,2,11,12, 15, 22.
The first topological index in chemistry was introduced by h. The wiener number has important applications in chemistry. Comparative evaluation of species diversity indices in the natural. Wiener and reverse wiener indices of some important classes of graphs are obtained. Many years later, some chemists got the same results. Oddvertexdegree trees maximizing wiener index boris furtula abstract. The contemporary literature cites wiener index as a topological parameter associated with treelike molecular graphs derived from organic molecular structures. Mathematical work on wiener index is started in 1970s 6. The wiener index is one of the oldest and most widely used topological indices in the quantitative structureproperty relationships qspr.
Wiener himself used the name path number,but denoted his quantity by w. A diversity index also called phylogenetic or simpsons diversity index is a quantitative measure that reflects how many different types such as species there are in a dataset a community and that can simultaneously take into account the phylogenetic relations among the individuals distributed among those types, such as richness, divergence or evenness. We denote the root vertex of h by h and the copy of h whose root is identified with the vertex t. Some hamiltonian properties and wiener index of graphs. Pages 6874 received 11 jan 2011, accepted 15 mar 2011, published online. The wiener index of random trees goetheuniversitat institut fur. Wiener index of eulerian graphs discrete applied mathematics.
The paper outlines the results known for w of trees. It has been one of main descriptors that correlate a chemical compounds molecular graph with experimentally gathered data regarding the compounds characteristics. There are no other apparent indexing or searching problems. Lastmaiden name first name sondauguter of spouse first name spouselast maiden name other married name date page numbers aad elias jeanne faye weiner springstroh 419, 420, 421, 422.
Adobe acrobat online services let you work with pdfs in any browser. Shannon wiener index is defined and given by the following function. The index value results from the addition of all paid and converted dividend points. The wiener index is defined as the summation of distances between all pairs of vertices in a graph or in a hypergraph.
A comparative study between the wiener index and several other topological indices as predictors for the boling points of saturated hydrocarbons called alkanes was done in reference 3, showing. Negative relationships between species richness and evenness. Box 60, 34000 kragujevac, serbia and montenegro received 7 july 2003 abstract. On the occasion of the fiftieth anniversary of the wiener. Given a graph g the corresponding wiener index or total distance wg is defined as the sum of the graphic distances reckoned across all possible vertexpairs of g. Bulletin of the australian mathematical society, vol. In this paper we investigate the maximum wiener index of trees with given degree sequences and the extremal trees which attain the maximum value. Dpsi log pi, where s is the total number of species in the sample, i is the total number of individuals in. In this paper, we consider relationships between hypertrees. Mathematics free fulltext wiener index of edge thorny graphs.
The final settlement price for derivative products is published on the last trading day on the third friday in december. In fact, the paw graph and square graph on four nodes are already indistinguishable using the wiener index both have value 8. We determine the wiener number of an important family of graphs, namely, the kneser graphs. Wiener literally means of vienna and is pronounced like veenuh in german. Pdf maximum wiener index of trees with given degree. Solving the equation for wt leads to the desired statement. The wiener index can be givenin terms ofthe mtiindex as follows. For example, in the drug design process, the aim is the construction of chemical. The wiener index of a graph g v, e, denoted by w g, was introduced in 1947 by chemist harold wiener 15 as the sum of distances between all.
A measure used by ecologists when a system contains too many individuals for each to be identified and examined. This index was the first topological index to be used in chemistry. Cannot search contents of pdf files using file explorer microsoft. Pdf the wiener index of random trees semantic scholar. Then the wiener index w is the halfsum of all distasums. In this paper, we provide a graph transformation named diametergrowing transformation relative to pendent edges, which increases. The wiener index is one of the oldest and most examined graphbased w molecular structure descriptors. For nonweighted simple graphs, the property of the wiener index have been achieved fruitful results. At that time, they use the concept of distance in graphs, which is actually the wiener index. Also, the shannonwiener index, simpson index, and mcintosh index. Create and convert pdfs online, reduce a file size, and more. Both modelsgraphtheoretical and hypergraphtheoreticalare used in mathematical chemistry for quantitatively studying physical and chemical properties of classical and nonclassical organic compounds.
Here we present result based on the wiener index for a graph to be hamiltonian or hamiltonconnected in this paper. Wiener and hyperwiener numbers in a single matrix journal. The wiener index of a graph is the sum of the distances between all pairs of vertices. Google first started indexing pdf files in 2001 and currently has hundreds of millions of pdf files indexed. Jan 10, 2014 the wiener index of the graph g, denoted by w w g, is the sum of distances between all pairs of vertices of g. Yet, wiener indices of eulerian graphs seem to have evaded the attention of. Wiener index of some graph operations sciencedirect. The numbers of non wiener unique connected graphs on, 2. Some of those formulas can also be applied to connected graphs. The well known physicochemist harold wiener 4, after whom the index was named, introduced this concept regarding the molecular distance and observed the existence of correlation between this index and numerous physicochemical properties of alkanes. On the defination of the hyperwiener index for cyclecontaining structures, j chem inf comput sci, 1995, 35. The wiener index of the graph g, denoted by w w g, is the sum of distances between all pairs of vertices of g.
Wiener index, hyperwiener index, harary index and hamiltonicity. Pdf wiener index of directed and weighted graphs by. The index is calculated and disseminated once a day. Pdf the extremal values of the wiener index of a tree. The hyper wiener index ww of a chemical tree t is defined as the sum of the products n 1n 2, over all pairs u, of vertices of t,wheren 1 and n. Then wg of a graph g may be corelated to the physicochemical properties of an organic compound represented as g. The wiener index of a connected graph g is the sum of distances between all pairs of vertices of g. On wiener index of graphs and their line graphs core. Lastmaiden name first name sondauguter of spouse first name spouselast maiden name other married name date page numbers aad elias jeanne faye weiner. It appears that for majority of chemical applications, the study of wiener index is restricted to acyclic molecular graphs although mathematical studies are reported for hexagonal.
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