• STRONG BLOCK DOMINATION IN GRAPHS

NAWAZODDIN U. PATEL*, M. H. MUDDEBIHAL

Abstract


For any graph, the  block graph  is a graph whose set of vertices is the union of the set of blocks of  in which two vertices are adjacent if and only if the corresponding blocks of  are adjacent. For any two adjacent vertices  and  we say that  strongly dominates  if .  A dominating set  of a graph  is a strong block dominating set of  if every vertex in   is strongly dominated by at least one vertex in . Strong block domination number  of  is the minimum cardinality of strong block dominating set of . In this paper, we study graph theoretic properties of  and many bounds were obtain in terms of elements of  and its relationship with other domination parameters were found.


Keywords


Dominating set/ Independent domination/ Block graph/ Line graph/ Roman domination/ Strong split domination/ Strong block domination.

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