Szeged index of bipartite unicyclic graphs

The Szeged index of a connected graph G is defined as the sum of products n۱(e|G)n۲(e|G) over all edges e = uv of G where n۱(e|G) and n۲(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.

Keywords:

Szeged index , unicyclic graphs , bipartite graphs , distance