Abstract
The domination integrity of a connected graph G= (V(G), E(G)) is denoted as DI(G) and defined by DI(G) = min{*S*+ m(G-S) : S is a dominating set } where m(G-S) is the order of a maximum component of G-S . We discuss domination integrity in the context of some graph operations like duplication of an edge by vertex and duplication of vertex by an edge.
Highlights
The vulnerability of communication network measures the resistance of network to the disruption of operation after the failure of certain station or communication links
The domination integrity of a connected graph G is denoted as DI G and defined by DI G min S m G S : S is a dominating set where m G S is the order of a maximum component of G S
We investigate the domination integrity for the graphs obtained by various graph operations
Summary
The vulnerability of communication network measures the resistance of network to the disruption of operation after the failure of certain station or communication links. The domination integrity of a connected graph G is denoted as DI G and defined by DI G min S m G S : S is a dominating set where m G S is the order of a maximum component of G S .
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