IJPAM: Volume 103, No. 3 (2015)

INVERSE DOMINATION NUMBER OF JUMP GRAPH

M. Karthikeyan$^1$, A. Elumalai$^2$
$^1$Bharathiar University
Coimbatore, 641046, INDIA
$^1$Department of Mathematics
Agni College of Technology
Chennai, 600130, INDIA
$^2$Department of Mathematics
Valliammai Engineering College
Chennai, 603203, INDIA


Abstract. Let $J(G) = (V, E)$ be a jump graph. Let $D$ be a minimum dominating set in a jump Graph $J(G)$. If $V-D$ contains a dominating set $D^\prime$ of $J(G)$, then $D^\prime$ is called an inverse dominating set with respect to $D$. The minimum cardinality of an inverse dominating set of a Jump graph $J(G)$ is called the inverse domination number of $J(G)$. In this paper We study the graph theoretic properties of inverse domination of Jump graph and its exact values for some standard graphs. The relation between inverse domination of Jump graph with other parameters is also investigated.

Received: April 30, 2015

AMS Subject Classification: 05C78

Key Words and Phrases: graph, circumference, diameter, domination, inverse domination number, jump graph

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DOI: 10.12732/ijpam.v103i3.9 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: 2015
Volume: 103
Issue: 3
Pages: 477 - 483


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