# Title

COMPLEMENTARY TREE PAIRED DOMINATION
VERTEX CRITICAL GRAPHS

# Authors

Department of Mathematics
S.K.R. Engineering College
Chennai, 600123, INDIA
Anna University
Chennai, 600025, INDIA
Department of Mathematics
Anna University, MIT Campus
Chennai, 600044, INDIA

# Abstract

A dominating set is a paired dominating set if the induced sub graph has a perfect matching. The minimum cardinality of a paired dominating set in is called the paired domination number of and is denoted by . The graph is paired domination vertex critical if for every vertex of that is not adjacent to a vertex of degree one, . If is -vertex critical and , then we say that is -vertex critical. In this paper we introduce the concept complementary tree paired domination vertex critical graph and also we present some upper and lower bounds of it. Furthermore, we construct the complementary tree paired domination vertex critical graph.

# History

Revised: November 23, 2016
Published: December 6, 2016

# AMS Classification, Key Words

AMS Subject Classification:
Key Words and Phrases: graph, paired domination, complementary tree, vertex critical graph

## Bibliography

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# How to Cite?

DOI: 10.12732/ijpam.v111i1.2 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: 2016
Volume: 111
Issue: 1
Pages: 9 - 15