Secure Domination in Lict Graphs

For any graph G = ( V , E ) , lict graph η ( G ) of a graph G is the graph whose vertex set is the union of the set of edges and the set of cut-vertices of G in which two vertices are adjacent if and only if the corresponding edges are adjacent or the corresponding members of G are incident. A secure lict dominating set of a graph η ( G ) , is a dominating set F ⊆ V ( η ( G ) ) with the property that for each v 1 ∈ ( V ( η ( G ) ) − F ) , there exists v 2 ∈ F adjacent to v 1 such that ( F − { v 2 } ) ∪ { v 1 } is a dominating set of η ( G ) . The secure lict dominating number γ s e ( η ( G ) ) of G is a minimum cardinality of a secure lict dominating set of G . In this paper many bounds on γ s e ( η ( G ) ) are obtained and its exact values for some standard graphs are found in terms of parameters of G . Also its relationship with other domination parameters is investigated.