On Zagreb eccentricity indices of cacti

Xiaodi Song, Jianping Li and Weihua He

Applied Mathematics and Computation, 2020, vol. 383, issue C

Abstract: For a connected graph G, the first Zagreb eccentricity index is defined as ξ1(G)=∑u∈V(G)e2(u), and the second Zagreb eccentricity index is defined as ξ2(G)=∑uv∈E(G)e(u)e(v), where e(u) is the eccentricity of u in G. Let C(n,k) be the class of all cacti of order n with k cycles. In this paper, we establish sharp lower bounds on Zagreb eccentricity indices of graphs in C(n,k) and determine the corresponding extremal graphs. What’s more, we characterize the graphs in C(n,k) with maximal Zagreb eccentricity indices, where 0≤k≤⌊n−12⌋.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:383:y:2020:i:c:s0096300320303258

DOI: 10.1016/j.amc.2020.125361

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