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Category: Issue 1

The inverse bondage number of a graph

YOGEESHA K M
Department of Mathematics, Government first Grade College, Davangere-577004, Karnataka (India)
N.D SONER
Department of Mathematics, Manasagangothri, Mysore-570006, Karnataka (India)

ABSTRACT:

The inverse bondage number b-1(G) of a graph G to be the cardinality of a smallest set E’ E of edges for which -1(G–E’)>-1(G). Thus, the inverse bondage number of G is the smallest number of edges whose removal will render every minimum inverse dominating set in G a “non inverse dominating set” set in the resultant spanning sub graph.

KEYWORDS: Domination numbers, Inverse domination numbers, Bondage number, 2000 mathematics subject classification:-05c69,05c70


The inverse bondage number b-1(G) of a graph G to be the cardinality of a smallest set E’ E of edges for which -1(G–E’)>-1(G). Thus, the inverse bondage number of G...