Vulnerability: Vertex Neighbor Integrity of Middle Graphs

Veena Mathad, Sultan Senan Mahde and Ali Mohammed Sahal

Department of Studies in Mathematics University of Mysore Manasagangotri, INDIA.


The vertex neighbor integrity of a connected graph G = (V,E) is denoted as V NI(G) and defined by where S is any vertex subversion strategy of G and m(G/S) is the number of vertices in the largest component of G/S. In this paper we obtain vertex neighbor integrity of middle graph of some standard graphs and combinations of these graphs. AMS Classifications: 05C40, 05C70, 05C76.

Keywords :Vulnerability, Stability, Vertex Neighbor Integrity, Middle Graph.

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