Minimal, vertex minimal and commonality minimal CN-dominating graphs

Document Type: Research Paper


University of Mysore


We define minimal CN-dominating graph $\mathbf {MCN}(G)$‎, ‎commonality minimal CN-dominating graph $\mathbf {CMCN}(G)$ and vertex minimal CN-dominating graph $\mathbf {M_{v}CN}(G)$‎, ‎characterizations are given for graph $G$ for which the newly defined graphs are connected‎. ‎Further serval new results are developed relating to these graphs‎.


Main Subjects

Anwar Alwardi, N. D. Soner and Karam Ebadi (2011). On the Common neighbourhood domination number. Journal Of Computer And Mathematical Sciences. 2 (3), 574-556
F. Harary (1969). Graph theory. Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London,.
T. W. Haynes, S. T. Hedetniemi and P. J. Slater (1998). Fundamentals of domination in graphs. Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc.. 208
S. M. Hedetneimi, S. T. Hedetneimi, R. C. Laskar, L. Markus and P. J. Slater (2006). Disjoint dominating sets in graphs.. Proc. Int. Conf. on Disc. Math., IMI-IISc. , 88-101
V. R. Kulli and B. Janakiram (1995). The Minimal Dominating Graph. 28, 12-15
V. R. Kulli, B. Janakiram and K. M. Niranjan (1996). The commonality minimal Dominating Graph. Indian J. Pure. appl. Math.. 27, 193-196
V. R. Kulli, B. Janakiram and K. M. Niranjan (2002). The Vertex Minimal Dominating Graph. Acta Ciencia Indica.. 28, 435-440
V. R. Kulli, B. Janakiram and K. M. Niranjan (2004). The Dominating Graph. Graph Theory Notes of New York, New York Academy of Sciences. 46, 5-8
H. B. Walikar, B. D. Acharya and E. Sampathkumar (1979). Recent developments in the theory of domination in graphs. Mehta Research instutute, Alahabad, MRI Lecture Notes in Math.. 1