General sum-connectivity index of trees and unicyclic graphs with fixed maximum degree

2018/07/11 by Jamil, M. K., Tomescu, I.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.04647

Abstract

The general sum-connectivity index of a graph G is defined as χ_α(G)=∑_{uv∈ E(G)} (d(u)+d(v))^α, where d(v) denotes the degree of the vertex v in G and α is a real number. In this paper it is deduced the maximum value for the general sum-connectivity index of n-vertex trees for -1.7036≤ α<0 and of n-vertex unicyclic graphs for -1≤ α<0 respectively, with fixed maximum degree \triangle . The corresponding extremal graphs, as well as the n-vertex unicyclic graphs with the second maximum general sum-connectivity index for n≥ 4 are characterized. This extends the corresponding results by Du, Zhou and Trinajsti' c [arXiv:1210.5043] about sum-connectivity index.

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