Tricyclic graphs with maximal revised Szeged index

2013/06/30 by Lily Chen, Xueliang Li, Chen, Lily +3
Mathematics · #05C12 #05C35 #05C90 #92E10 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C12 #msc:05C35 #msc:05C90 #msc:92E10

paper · pdf · doi:10.48550/arxiv.1307.0192

14 pages. arXiv admin note: text overlap with arXiv:1104.2122

arxiv created 2013/06/30 · arxiv updated 2013/07/02

Abstract

The revised Szeged index of a graph G is defined as Sz^*(G)=∑_{e=uv ∈ E}(n_u(e)+ n₀(e)/2)(n_v(e)+ n₀(e)/2), where n_u(e) and n_v(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, and n₀(e) is the number of vertices equidistant to u and v. In this paper, we give an upper bound of the revised Szeged index for a connected tricyclic graph, and also characterize those graphs that achieve the upper bound.

Citations

• Bicyclic graphs with maximal revised Szeged index

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