Applications of l Distance Domination of Semigraph
摘要
Semigraphs are an efficient mathematical tool for precisely modeling and analyzing complicated systems and interactions. Let \(S=(V_S,X_S)\) be a connected semigraph. A subset J of \(V_S\) is called l dominating set of S if for all \(v \in V_S-J\) there exist \(u\in J\) such that \(d(v,u)\le l\) . l domination number \(\gamma _{l}(S)\) is the minimum cardinality of l dominating set of S. In addition, if the set J is a subset of the set of all end vertices of S then J is called (l, e) dominating set of S and (l, e) domination number \(\gamma _{l}^{e}(\) S) is the minimum cardinality of (l, e) dominating set of S. In this paper, we try to determine l and (l, e) domination number of some classes of semigraphs including corona product of semigraphs, friendship semigraph, fan semigraph helm semigraph, wheel semigraph, etc. In addition, practical applications of l distance domination of semigraphs are discussed.