SPLIT DOMINATION VERTEX CRITICAL AND EDGE CRITICAL GRAPHS

Girish V R, Usha P

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(G􀀀v) < 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.


Full Text:

PDF

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.




DOI: https://doi.org/10.22342/jims.26.1.772.55-63

Refbacks

  • There are currently no refbacks.



Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243
Email: jims.indoms@gmail.com


p-ISSN: 2086-8952 | e-ISSN: 2460-0245


Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats