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.
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