the Hosoya polynomial of these graphs. c 2001 Elsevier Science B.V. All rights reserved. 1. The name Wiener number or Wiener index is nowadays in standard use in chemistry the grid, sun and generalized wheel, respectively. 10 Apr 2015 Organic Molecules, Edge Wiener Index, Fan Graph, Wheel Graph, Gear Fan Graph, Gear Wheel Graph, r-Corona Graph. Received: March 23 Abstract: The Wiener index of a graph G denoted by W(G) is the sum of distances between Proof If Wn is a wheel graph with n vertices, m edges and n. ∑ i=1. The Wiener index is a graphical invariant that has found extensive application in chemistry. We define the complete graph, path, cycle, and wheel on n vertices 1 Jan 2018 of path graph, star graph, wheel graph, gear graph, helm graph are derived. The Wiener index W(G) is a distance-based topological invariant
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WIENER INDEX OF A GRAPH the positive side, it is claimed that QSPR and QSAR techniques are much less expensive than any other method of gaining information about the properties of chemical compounds. In recent times, QSAR has become a popular computational biology paradigm in modern drug The Wiener index W(G) of a graph G is a distance-based topological index defined as the sum of distances between all pairs of vertices in G. It is shown that for λ=2 there is an infinite family of planar bipartite chemical graphs G of girth 4 with the cyclomatic number λ, but their line graphs are not chemical graphs, and for λ⩾2 there are two infinite families of planar nonbipartite First mathematical definition of Wiener index, based on the concept of graph- theoretical distance as encoded in the distance matrix [11] is due to Hosoya [5] since its initiation the wiener index was used in a numerous structure-property studies [15].Wiener index was developed by the American Reciprocal complementary Wiener index of a graph G is defined i j as RCW ( G ) = ∑i< j 1+ D1−dij , where dij is the distance between two vertices vi and v j and D is the diameter of G . In this paper we obtain bounds for the reciprocal Wiener index and reciprocal complementary Wiener index of line graphs. An exact expression for the edge-Wiener index of these graphs would be rather unpleasant. But if q ≫ n, then their edge-Wiener index is approximately W e (G) = (1 + o (1)) (q 2 n − 3 n − 1 − q (n − 1)). In order to determine an asymptotically sharp upper bound on the edge-Wiener index of a graph of given order, we first find a bound
Journal of Chemical and Pharmaceutical Research, 2016, 8(3):51-57 corresponding indices of the subdivision graph and the line graph subdivision graph of wheel graph. Keywords: Topological indices, Schultz indices, Schultz polynomial, subdivision graph, line graph. Wiener index is one of the topological indices that correlate with some
dices, a particular case of Smarandache-Zagreb index of a graph changes The Wiener index W belongs among the oldest graph-based structure-descriptors length k and a wheel graph Wn+1 [7] is defined as the graph K1 + Cn, where K1 Keywords: Wiener index, average distance, generalized prisms, uniform n-wheel split graph, uniform n-star split graph, cyclic split graph. c JS Publication. 1. In the mathematical discipline of graph theory, a wheel graph is a graph formed by connecting Retrieved from "https://en.wikipedia.org/w/index.php?title= Wheel_graph&oldid=938417281". Categories: Parametric families of graphs · Planar have been introduced, Wiener index is one of the topological indices that modified Schultz topological indices of subdivision graph of the wheel graph S( Wn) A generating function, which we call Wiener polynomial is also defined. In this paper, Wiener index and Wiener polynomial of Wheel graph, Friendship graph the Hosoya polynomial of these graphs. c 2001 Elsevier Science B.V. All rights reserved. 1. The name Wiener number or Wiener index is nowadays in standard use in chemistry the grid, sun and generalized wheel, respectively.
Abstract: The Wiener index of a graph G denoted by W(G) is the sum of distances between Proof If Wn is a wheel graph with n vertices, m edges and n. ∑ i=1.
The Wiener index W(G) of a graph G is a distance-based topological index defined as the sum of distances between all pairs of vertices in G. It is shown that for λ=2 there is an infinite family of planar bipartite chemical graphs G of girth 4 with the cyclomatic number λ, but their line graphs are not chemical graphs, and for λ⩾2 there are two infinite families of planar nonbipartite First mathematical definition of Wiener index, based on the concept of graph- theoretical distance as encoded in the distance matrix [11] is due to Hosoya [5] since its initiation the wiener index was used in a numerous structure-property studies [15].Wiener index was developed by the American
23 Oct 2017 The Wiener index W(G), the Balaban index J(G) and the complete bipartite and complete multipartite graphs, moreover wheel graphs and
Keywords: Wiener index, average distance, generalized prisms, uniform n-wheel split graph, uniform n-star split graph, cyclic split graph. c JS Publication. 1. In the mathematical discipline of graph theory, a wheel graph is a graph formed by connecting Retrieved from "https://en.wikipedia.org/w/index.php?title= Wheel_graph&oldid=938417281". Categories: Parametric families of graphs · Planar have been introduced, Wiener index is one of the topological indices that modified Schultz topological indices of subdivision graph of the wheel graph S( Wn) A generating function, which we call Wiener polynomial is also defined. In this paper, Wiener index and Wiener polynomial of Wheel graph, Friendship graph