Connected cototal domination number of a graph

Document Type : Research Paper


1 Karnatak University

2 Karnatak University, Dharwad


A dominating set $D \subseteq V$ of a graph $G = (V,E)$ is said to be a connected cototal dominating set if $\langle D \rangle$ is connected and $\langle V-D \rangle \neq \varnothing $‎, ‎contains no isolated vertices‎. ‎A connected cototal dominating set is said to be minimal if no proper subset of $D$ is connected cototal dominating set‎. ‎The connected cototal domination number $\gamma_{ccl}(G)$ of $G$ is the minimum cardinality of a minimal connected cototal dominating set of $G$‎. ‎In this paper‎, ‎we begin an investigation of connected cototal domination number and obtain some interesting results‎.


Main Subjects

H. Chen, X. Chen and X. Tan (2011). On k-connected restrained domination in graphs. Ars Combin.. 98, 387-397 E. J. Cockayne and S. T. Hedetniemi (1977). Towards a theory of domination in Graphs,. Networks. 7, 247-261 G. S. Domke, J. H. Hatting, S. T. Hedetniemi, R. C. Laskar and L. R. Markus (1999). Restrained domination in graphs. Discrete Math.. 203, 61-69 E. J. Cockayne, R. M. Dawes and S. T. Hedetniemi (1980). Total domination in graphs,. Networks. 10, 211-219 F. Harary (1969). Graph Theory. Addison-Wesley, Reading. T. W. Haynes, S. T. Hedetniemi and P. J. Slater (1998). Fundamentals of domination in graphs. Marcel Dekker, Inc., New York. M. A. Henning (1999). Graphs with large restrained domination number. Discrete Math. 197/198, 415-429 V. R. Kulli, B. Janakiram and R. R. Iyer (1999). The cototal domination number of a graph,. J. Discrete Math. Sci. Cryptography. 2, 179-184 V. R. Kulli and B. Janakiram (2000). The nonsplit domination number of a graph. Indian. J. Pure. Appl. Math.. 31, 545-550 E. Sampathkumar and H. B. Walikar (1979). The connected domination number of a graph,. J. Math. Phys. Sci.. 13, 607-613