## The inverse bondage number of a graph

#### AUTHOR AND AFFILIATION

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)

#### KEYWORDS:

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

January 2019

1-3

#### ISSN:

2319-8044 (Online) – 2231-346X (Print)

Vol.31 – No.1

#### DOI:

http://dx.doi.org/10.22147/jusps-A/310101

#### 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.

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