Characterizations of Connected Perfect Domination in Graphs
DOI:
https://doi.org/10.53555/ms.v5i3.820Keywords:
Domination, Connected Domination, Perfect Domination, connected perfect dominationAbstract
A subset of is a connected perfect dominating set of if is both connected and perfect dominating set of . The connected perfect domination number of denoted by is the cardinality of the smallest connected perfect dominating set of . A connected perfect dominating set of with cardinality equal to is called a of . This paper shows some charaterization of a connected dominating set and the values or bounds of the parameter were determined. It also characterizes the connected perfect dominating set in the join and corona of graphs and the corresponding values of the parameter were also determined.
Downloads
References
M. Chellali, F. Maffray, and K. Tablennehas, Connected domination DOT-critical graphs. Contributions to Discrete Mathematics, 5 (2010), no. 2, 11–25.
I. Dejter, A. Delgado, Perfect domination in rectangular grid graphs. Australasian J. of Combinatorics, accepted for publication.
C.E. Go, and S.R. Canoy, Jr., Domination in the corona and join of graphs. International Mathematical Forum, 6 (2011), no. 16, 763–771.
M. Livingston and Q. F. Stout, Perfect Dominating Sets. Congr. Numer., 79 (1990), 187–203.
B.F.Tubo, S.R.Canoy, Restrained Perfect Domination in Graphs. International Journal of Mathematical Analysis Vol. 9, 2015, no. 25, 1231–1240.
E.Sampathkumar and H.B. Walikar, The connected domination number of a graph. Math. Physi. Sci. 13 (1979), 607–613.
C. Yen, R.C.T. Lee, The weighted perfect domination problem and its variants. Discrete Applied Mathematics 66 (1996) 147–160.
