(2, 2) – Total Domination in Graphs

AUTHOR AND
AFFILIATION

KEYWORDS:

-

Issue Date:

April 2014

Pages:

15-18

ISSN:

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

Source:

Vol.26 – No.1

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DOI:

jusps-A

ABSTRACT:

A set S of vertices in a graph G=(V, E) is a (2, 2)-total dominating set of G if every vertex in V is adjacent to at least 2 vertices in S and at least 2 vertices in V – S. The minimum cardinality of a (2, 2)-total dominating set is called the (2, 2)-total domination number of G and is denoted by t2,2(G). In this paper, we initiate a study of (2, 2)-total domination in graphs. Some bounds on t2,2(G) are found and its exact values for some standard graphs are obtained.

Copy the following to cite this Article:

, “(2, 2) – Total Domination in Graphs”, Journal of Ultra Scientist of Physical Sciences, Volume 26, Issue 1, Page Number 15-18, 2016


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, “(2, 2) – Total Domination in Graphs”, Journal of Ultra Scientist of Physical Sciences, Volume 26, Issue 1, Page Number 15-18, 2016

Available from: http://www.ultrascientist.org/paper/159/


A set S of vertices in a graph G=(V, E) is a (2, 2)-total dominating set of G if every vertex in V is adjacent to at least 2 vertices in S and at least 2 vertices in V – S. The minimum cardinality of a (2, 2)-total dominating set is called the (2, 2)-total domination number of G and is denoted by t2,2(G). In this paper, we initiate a study of (2, 2)-total domination in graphs. Some bounds on t2,2(G) are found and its exact values for some standard graphs are obtained.