Hub-integrity of splitting graph and duplication of graph elements

Abstract

The hub-integrity of a graph G = (V (G), E(G)) is denoted as HI(G) and defined by HI(G) = min{|S| + m(G ? S), S is a hub set of G}, where m(G ? S) is the order of a maximum component of G ? S. In this paper, we discuss hub-integrity of splitting graph and duplication of an edge by vertex and duplication of vertex by an edge of some graphs.