Szeged index of bipartite unicyclic graphs

Abstract

The Szeged index of a connected graph G is defined as the sum of products n₁(e|G)n₂(e|G) over all edges e = uv of G where n₁(e|G) and n₂(e|G) 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 In this paper, we determine the n-vertex bipartite unicyclic graphs with the first, the second, the third and the fourth smallest Szeged indices.