Computation of Gutman index of some cactus chains

Abstract

Let G be a finite connected graph of order n. The Gutman index Gut(G) of G is defined as ∑ {x,y}⊆V (G) deg(x)deg(y)d(x, y), where deg(x) is the degree of vertex x in G and d(x, y) is the distance between vertices x and y in G. A cactus graph is a connected graph in which no edge lies in more than one cycle. In this paper we compute the exact value of Gutman index of some cactus chains.

General Zagreb index of some cactus chains

“…The graph Q(m, n) is derived from K m and m copies of K n by identifying every vertex of K m with a vertex of one K n [5]. The example of Q(m, n) graph is shown in Figure 5.…”

“…Recently, Sadeghieh et al in [1] derived Hosoya polynomial of some cactus chain and studied some degree based topological indices. we refer the reader [2][3][4][5] for further study about cactus graph. In this work, we study the mathematical property of general Zagreb index or (a, b)-Zagreb index of some general ortho and para cactus chains and hence consider their special cases such as triangular chain cactus T n , ortho chain square cactus O n and para-chain square cactus Q n , where n denote the length of the chain and then we derive some explicit expressions of the same for other degree based topological indices such as Zagreb indices, forgotten index, redefined Zagreb index, general first Zagreb index, general Randić index, symmetric division index for particular values of a and b of general Zagreb index.…”

M-polynomial of some cactus chains and their topological indices

“…The graph Q(m, n) is derived from K m and m copies of K n by identifying every vertex of K m with a vertex of one K n [11]. Here we compute the M− polynomial of the graph Q(m, n) and derive some other topological indices from it.…”

“…For ortho-chain square cactus the cut vertices are adjacent and a para-chain square cactus their cut vertices are not adjacent. Recent study on some cactus chain can be found in [9][10][11] and references cited therein. For undefined graph theoretic terminology used in this paper can be found in [12].…”

Gourava and Hyper-Gourava Indices of Some Cactus Chains

“…The Gourava and hyper-Gourava indices of various generic ortho and para cactus chains are studied in this paper, and particular situations such as the triangular chain cactus T n , ortho-chain square cactus O n , and para-chain square cactus Q n are considered. Latest investigations on several cactus chains can be found in [1,3,13,14] and references cited therein. For undefined terms and notations refer to [5].…”