Eccentric connectivity coindex of bipartite graphs

Abstract

The eccentric connectivity coindex of a graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the vertex set of [Formula: see text], [Formula: see text] is the edge set of [Formula: see text], [Formula: see text] is the eccentricity of [Formula: see text] and [Formula: see text] is the degree of [Formula: see text] in [Formula: see text]. We present lower bounds on the eccentric connectivity coindex for bipartite graphs of given order and vertex connectivity, order and matching number, order and odd diameter. The extremal graphs are presented as well. To the best of our knowledge, our extremal graphs of given order and vertex connectivity are not extremal graphs for any other research problem in graph theory.