Abstract
The revised Szeged index of a graph G is defined as Sz∗(G)=∑e=uv∈E(nu(e)+n0(e)/2)(nv(e)+n0(e)/2), 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, 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.
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