On extremal cacti with respect to the Szeged index

Shujing Wang

Applied Mathematics and Computation, 2017, vol. 309, issue C, 85-92

Abstract: The Szeged index of a graph G is defined as Sz(G)=∑e=uv∈Enu(e)nv(e), where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. A cactus is a graph in which any two cycles have at most one common vertex. Let C(n,k) denote the class of all cacti with order n and k cycles, and Cnt denote the class of all cacti with order n and t pendant vertices. In this paper, a lower bound of the Szeged index for cacti of order n with k cycles is determined, and all the graphs that achieve the lower bound are identified. As well, the unique graph in Cnt with minimum Szeged index is characterized.

Keywords: Szeged index; Cactus; Pendent vertex (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:309:y:2017:i:c:p:85-92

DOI: 10.1016/j.amc.2017.03.036

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