On the extremal cactus graphs for variable sum exdeg index with a fixed number of cycles

Abstract

The variable sum exdeg index, introduced by Vuki cevi c [Croat. Chem. Acta 84 (2011) 87-91] for predicting the octanol-water partition coefficient of certain chemical compounds, of a graph G is defined as SEI a ðGÞ ¼ P v2VðGÞ d v a dv , where a is any positive real number different from 1, V(G) is the vertex set of G and d v denotes the degree of a vertex v. A connected graph G is a cactus if and only if every edge of G lies on at most one cycle. For n > 3 and k ! 0, let C n, k be the class of all n-vertex cacti with k cycles. The present paper is devoted to find the graphs with minimal and maximal SEI a values among all the members of the graph class C n, k for a > 1.

Conjugated tricyclic graphs with maximum variable sum exdeg index

“…In [14] , the author investigated sharp lower and upper bounds on for conjugated bicyclic graphs. The author et al investigated extremal values of for cactus graphs with fixed number of cycles [6] . We refer the following papers to see mathematical properties and chemical application of this index [1] , [19] , [21] .…”

On the variable sum exdeg index/coindex of graphs

“…The problem of finding graphs having the extremum values of the variable sum exdeg index of the trees of a fixed order and with the vertices having prescribed degrees was attacked in [11]. Additional recent results about the variable sum exdeg index can be found in the papers [3,7,9,13,18].…”

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“…Hosoya index, Randic′ index, Zagreb index, and Szeged index [2][3][4] are some of the commonly known topological indices used for investigating the Quantitative Structure-Activity Relationship(QSAR) and Quantitative Structure-Property Relationships(QSPR) of chemical graphs and nanostructures. Over the years, many variations of these indices have been introduced and studied by various authors [5][6][7][8][9][10][11][12][13]. In particular, many authors have worked on constructing graph-theoretic polynomials based on which some of these topological indices can be found [14][15][16][17][18][19][20][21].…”