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Vulnerability: Integrity of a Middle Graph

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Author(s): Aysun Aytaç | Şebnem Çelik

Journal: Selçuk Journal of Applied Mathematics
ISSN 1302-7980

Volume: 9;
Issue: 1;
Start page: 49;
Date: 2008;
Original page

Keywords: Vulnerability | Graph Theory | Connectivity | Stability | Integrity | Middle graph of a graph.

ABSTRACT
A communication network can be considered to be highly vulnerable to disruption if the destruction of a few elements can result in no member's being able to communicate with very many others. This idea suggests the concept of the integrity of a graph. The vertex-integrity of a graph G, denoted I(G), is defined by I(G)=min{|S|+m(G-S)} where m(G-S) denotes the maximum order of a component of G-S. In this paper we consider the integrity of middle graphs of specific families of graphs and combinations of these graphs.

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