Strong Domination Number of Some Wheel Related Graphs

S K Vaidya, R N Mehta


A vertex $u$ strongly dominates $v$ or $v$ weakly dominates $u$ if $uv \in E(G)$ and $deg(u) \geq deg(v)$ in graph $G$. A subset $D$ is a strong(weak) dominating set if every vertex $v \in V(G)-D$ is strongly(weakly) dominated by some $u$ in $D$. The minimum cardinality of a strong(weak) dominating set is the strong(weak) domination number. In this paper we explore the concept of strong domination number and investigate strong domination number of some wheel related graphs.

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R. Boutrig and M. Chellali, A Note on a Relation Between the Weak and Strong Domination

Numbers of a Graph, Opuscula Mathematica, 32 (2012), 235-238.

R. B. Allan and R. Laskar, On Domination and Independent Domination Numbers of a

Graph, Discrete Mathematics, 23 (1978), 73-76.

E. J. Cockayne and S. T. Hedetniemi, Towards a Theory of Domination in Graphs, Networks,

(1977), 247-261.

G. S. Domke, J. H. Hattingh, L. R. Markus and E. Ungerer, On Parameters Related to

Strong and Weak Domination in Graphs, Discrete Mathematics, 258 (2002), 1-11.

F. Harary, Graph Theory, Addison - Wesley, Reading, Massachusetts, 1969.

J. H. Hattingh, M. A. Henning, On Strong Domination in Graphs, J. Combin. Math.

combin. Comput., 26 (1998), 33-42.

D. A. Holton and J. Sheehan, The Petersen Graph, Australian Mathematical Society Lecture

Notes 7, Cambridge University Press, 1993.

T. W. Haynes, S. T. Hedetniemi and P. J. Slater , Fundamentals of Domination in Graphs,

Marcel Dekker, New York, 1998.

D. Rautenbach, Bounds on the Strong Domination Number, Discrete Mathematics,

(2000), 201-212.

D. Rautenbach, The Influence of Special Vertices on Strong Domination, Discrete Mathematics,

/198 (1999), 683-690.

E. Sampathkumar and L. Pushpa Latha, Strong Weak Domination and Domination Balance

in a Graph, Discrete Mathematics, 161 (1996), 235-242.

V. Swaminathan and P. Thangaraju, Strong and Weak Domination in Graphs, Electronic

Notes in Discrete Mathematics, 15 (2003), 213-215.


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