Main Article Content
Abstract
A dominating set D of a graph G = (V;E) is a split dominating set if
the induced graph hV Di is disconnected. The split domination number s(G)
is the minimum cardinality of a split domination set. A graph G is called vertex
split domination critical if s(Gv) < s(G) for every vertex v 2 G. A graph G is
called edge split domination critical if s(G + e) < s(G) for every edge e in G. In
this paper, whether for some standard graphs are split domination vertex critical or
not are investigated and then characterized 2- ns-critical and 3- ns-critical graphs
with respect to the diameter of a graph G with vertex removal. Further, it is shown
that there is no existence of s-critical graph for edge addition.
Article Details
References
- S.Arumugam and J.Paulraj Joesph, Domination in Subdivision graphs, Journal of Indian Mathematical Society 62(1-4) (1996), 274-282.
- David p.summer and Pattie blitch, Domination critical graph, Journal of combinatorial theory series B. 34 (1983), 65-76.
- F.Harary, Graph theory, Addison-wesley. reading Mass.
- V.R.Kulli, B.Janikiram, , The split domination number of a graph, Graph Theory Notes of New York Academy of Sciences. XXXII (1997), 16-19
- Magdalena Lemanska, Agnieszka Patyk, Weakly Connected Domination Critical graphs, Opuscula Mathematica 28 n0.3 (2008), 325-330
- Robert C.Brigham, Phyllis Z.Chinn, Ronald D. Dutton, Vertex domination critical graphs, 18 no 3.(1988), 173-179.
- D.P.Sumner, Critical concepts in domination, Discrete Math. 86(1990), 33-46.
- Teresa W.Haynes, Stephen T.Hedetniemi, Peter J Slater, Fundamental of domination of graphs Marcel Dekker, Inc.Newyork ,(1988).
- Xue-Gang, Liang Sun, De-Xiang Ma, Connected Domination Critical graphs, Applied Mathematics. 17 (2004), 503-507.
References
S.Arumugam and J.Paulraj Joesph, Domination in Subdivision graphs, Journal of Indian Mathematical Society 62(1-4) (1996), 274-282.
David p.summer and Pattie blitch, Domination critical graph, Journal of combinatorial theory series B. 34 (1983), 65-76.
F.Harary, Graph theory, Addison-wesley. reading Mass.
V.R.Kulli, B.Janikiram, , The split domination number of a graph, Graph Theory Notes of New York Academy of Sciences. XXXII (1997), 16-19
Magdalena Lemanska, Agnieszka Patyk, Weakly Connected Domination Critical graphs, Opuscula Mathematica 28 n0.3 (2008), 325-330
Robert C.Brigham, Phyllis Z.Chinn, Ronald D. Dutton, Vertex domination critical graphs, 18 no 3.(1988), 173-179.
D.P.Sumner, Critical concepts in domination, Discrete Math. 86(1990), 33-46.
Teresa W.Haynes, Stephen T.Hedetniemi, Peter J Slater, Fundamental of domination of graphs Marcel Dekker, Inc.Newyork ,(1988).
Xue-Gang, Liang Sun, De-Xiang Ma, Connected Domination Critical graphs, Applied Mathematics. 17 (2004), 503-507.