Endedge block domination in graphs

Abstract

For any graph G (V, E ) , a block graph B(G ) is a graph whose vertices are corresponding to the blocks of G and two vertices in B(G ) are adjacent whenever the corresponding blocks contain a common cutvertex in G . An edge dominating set  of a block graph B(G ) is an endedge block dominating set if    contains all endedges of B(G ) . The endedge block domination number (G ) is the minimum cardinality of an endedge block dominating set . In this paper some bounds for (G ) are obtained in terms of elements of G . Further exact values of   (G ) for some standard graphs and relationships with other dominating parameters were obtained.