DOMINATION EDGE INTEGRITY OF GRAPHS


Kılıç E. , Beşirik A.

Advanced Mathematical Models & Applications, vol.3, no.3, pp.234-238, 2018 (Refereed Journals of Other Institutions)

  • Publication Type: Article / Article
  • Volume: 3 Issue: 3
  • Publication Date: 2018
  • Title of Journal : Advanced Mathematical Models & Applications
  • Page Numbers: pp.234-238

Abstract

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 .