Total Domination Polynomial of A Graph

Authors

  • B. Chaluvaraju Department of Mathematics, Bangalore University, Central College Campus, Bangalore 560001
  • V. Chaitra Department of Mathematics, Bangalore University, Central College Campus, Bangalore 560001

DOI:

https://doi.org/10.26713/jims.v6i2.256

Keywords:

Graph, Domination number, Sign domination number

Abstract

A total domination polynomial of a graph $G$ of order $n$ is the polynomial $D_{td}(G,x) =\sum^n_{t=\gamma_{td}(G)}d_{td}(G,t)x^t$, where $d_{td}(G,t)$ is the number of total dominating sets of $G$ of cardinality $t$. In this paper, we present various properties of total domination polynomial of graph $G$. Also determine the total domination polynomial of some graph operations.

Downloads

Download data is not yet available.

References

S. Alikhani and Y. H. Peng, Introduction to domination polynomial of a graph, Ars Combinatoria 114(2014), 257-266.

S. Alikhani, On the Domination Polynomial of Some Graph Operations, ISRN Combin. 2013, Article ID 146595.

E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10(1980), 211-219.

I. Gutman and B. Borovicanin, Nullity of graphs: An updated survey, in Selected topics on applications of graph spectra, Math. Inst., Belgrade (2011), 137-154.

F. Harary, Graph Theory, Addison-Wesley, Reading Mass (1969).

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc., New York (1998).

Michael A. Henning, A survey of selected recent results on total domination in graphs, Discrete Mathematics 309(2009), 32-63.

N. D. Soner, B. Chaluvaraju and B. Janakiram, Total split domination in graphs, Far East Journal of Appl. Math. 6(1) (2002), 89-95.

N. D. Soner and B. Chaluvaraju, Total non-split domination in graphs, J. of Math. Ed. 38(2) (2004), 77-80.

Downloads

Published

2014-12-31
CITATION

How to Cite

Chaluvaraju, B., & Chaitra, V. (2014). Total Domination Polynomial of A Graph. Journal of Informatics and Mathematical Sciences, 6(2), 87–92. https://doi.org/10.26713/jims.v6i2.256

Issue

Section

Research Articles