IJPAM: Volume 87, No. 6 (2013)

TOTAL BONDAGE NUMBER OF CERTAIN GRAPHS

Jasintha Quadras$^1$, A. Sajiya Merlin Mahizl$^2$
$^{1,2}$Stella Maris College
Chennai, Tamilnadu, 600 086, INDIA


Abstract. A set $D$ of a vertices in a graph $G=(V, E)$ is said to be a total dominating set of $G$ if every vertex in $V$ is adjacent to some vertex in $D$. The total domination number $\gamma_{t}(G)$ is the minimum cardinality of a total dominating set. If $\gamma_{t}(G)\neq \vert V(G)\vert$, the minimum cardinality of a set $E_{0}\subseteq E(G)$, such that $ G-E_{0}$ contains no isolated vertices and $\gamma_{t}(G-E_{0})>\gamma_{t}(G)$, is called the total bondage number of $G$. This paper determines the exact values of total bondage number of Wheel graph, Helm graph, Windmill graph, Circular necklace and Friendship graph.

Received: September 6, 2013

AMS Subject Classification: 05C69

Key Words and Phrases: total dominating set, total domination number, total bondage number

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DOI: 10.12732/ijpam.v87i6.15 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 6