Neighborhood connected perfect domination in graphs

Main Article Content

Kulandai Vel M.P.
Selvaraju P.
Sivagnanam C.

Abstract

Let $G = (V, E)$ be a connected graph. A set $S$ of vertices in $G$ is a perfect dominating set if every vertex $v$ in $V-S$ is adjacent to exactly one vertex in $S$. A perfect dominating set $S$ is said to be a neighborhood connected perfect dominating set (ncpd-set) if the induced subgraph $$ is connected. The minimum cardinality of a ncpd-set of $G$ is called the neighborhood connected perfect domination number of $G$ and is denoted by $\gamma_{ncp}(G)$. In this paper we initiate a study of this parameter.

Article Details

How to Cite
M.P., K. V., P., S., & C., S. (2012). Neighborhood connected perfect domination in graphs. Tamkang Journal of Mathematics, 43(4), 557–562. https://doi.org/10.5556/j.tkjm.43.2012.839
Section
Papers
Author Biographies

Kulandai Vel M.P., Anna University

Department of Mathematics, St. Joseph’s College of Engineering, Chennai-600119, India.

Selvaraju P.

Department of Mathematics, VELTECH (Owned by RS Trust), No. 60, Veltech-Avadi Road, Chennai-600062, Tamilnadu,India.

Sivagnanam C.

School of Sciences, Birla Institute of Technology, Kingdom of Bahrain.

References

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T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs-Advanced Topics, Marcel Dekker, Inc., New York, 1997.