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

Issue Date:

January 2019

Pages:

1-3

ISSN:

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

Source:

Vol.31 – No.1

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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.

Copy the following to cite this Article:

Y. K. M; N. Soner, “The inverse bondage number of a graph”, Journal of Ultra Scientist of Physical Sciences, Volume 31, Issue 1, Page Number 1-3, 2019


Copy the following to cite this URL:

Y. K. M; N. Soner, “The inverse bondage number of a graph”, Journal of Ultra Scientist of Physical Sciences, Volume 31, Issue 1, Page Number 1-3, 2019

Available from: http://www.ultrascientist.org/paper/1509/the-inverse-bondage-number-of-a-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.