Article ID Journal Published Year Pages File Type
4949931 Discrete Applied Mathematics 2016 6 Pages PDF
Abstract
The edge revised Szeged index Sze∗(G) is defined as Sze∗(G)=∑e=uv∈E(mu(e)+m0(e)/2)(mv(e)+m0(e)/2), where mu(e) and mv(e) are, respectively, the number of edges of G lying closer to vertex u than to vertex v and the number of edges of G lying closer to vertex v than to vertex u, and m0(e) is the number of edges equidistant to u and v. In this paper, we give an upper bound of the edge revised Szeged index for a connected bicyclic graphs with size m≥5, that is, Sze∗(G)≤{(m3−4m+16)/4,if  m  is odd ,(m3−4m+18)/4,if  m  is even with equality if and only if G is the graph obtained from the cycle Cm−2 by duplicating a single vertex.
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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