Research Information System
Advanced Mathematical Models & Applications, vol.3, no.3, pp.234-238, 2018 (Refereed Journals of Other Institutions)
In an analysis of the vulnerability of a communication network to disruption, the most important two
questions that come to mind are (i) what is the number of elements that are not functioning and (ii) what is the size
of the largest remaining group in which mutual communication still continues. Integrity is one of the well-known
vulnerability measures interested in these questions. Depending on network models new vulnerability measures
take a great role in any failure not only on nodes also on links which have special properties. Domination is an
another famous concept in network design. Sundareswaran and Swaminathan introduced domination integrity
such as DI(G) = min{ |S| + m(G − S) : S ⊂ V (G)} where m(G − S) denotes the order of a largest component
of graph G − S and S is a dominating set of G. In this work we define a new measure edge domination integrity
of a connected and undirected graph G such as DI
′
(G) = min{ |S| + m(G − S) : S ⊆ E(G)} where m(G − S)
is the order of a maximum component of G − S and S is an edge dominating set. In this paper we present some
results concerning this parameter on graph structures Pn, Cn, Km,n, K1,n .