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On Zagreb eccentricity indices of cacti

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  • Song, Xiaodi
  • Li, Jianping
  • He, Weihua

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⌋.

Suggested Citation

  • Song, Xiaodi & Li, Jianping & He, Weihua, 2020. "On Zagreb eccentricity indices of cacti," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    • Handle: RePEc:eee:apmaco:v:383:y:2020:i:c:s0096300320303258
    DOI: 10.1016/j.amc.2020.125361
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    1. Li, Jianping & Zhang, Jianbin, 2019. "On the second Zagreb eccentricity indices of graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 180-187.
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