Some useful lemmas on the edge Szeged index

2018/05/17 by He, Shengjie
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.06578

Abstract

The edge Szeged index of a graph G is defined as Sz_e(G)=∑_{uv∈ E(G)}m_u(uv|G)m_v(uv|G), where m_u(uv|G) (resp., m_v(uv|G)) is the number of edges whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), respectively. In this paper, we characterize the graph with minimum edge Szeged index among all the unicyclic graphs with given order and diameter.

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