Domination Uniform Subdivision Number of Graph
![]() |
International Journal of Mathematics Trends and Technology (IJMTT) | ![]() |
© 2015 by IJMTT Journal | ||
Volume-27 Number-1 |
||
Year of Publication : 2015 | ||
Authors : M. K. Angel Jebitha |
||
![]() |
M. K. Angel Jebitha "Domination Uniform Subdivision Number of Graph", International Journal of Mathematics Trends and Technology (IJMTT). V27(1):1-5 November 2015. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.
Abstract
Let G = (V, E) be a simple undirected graph. A subset
D of V(G) is said to be dominating set if every vertex
of V(G) − D is adjacent to at least one vertex in D.
The minimum cardinality taken over all minimal dominating
sets of G is the domination number of G and
is denoted by g(G). The domination uniform subdivision
number of G is the least positive integer k such
that the subdivision of any k edges from G results in a
graph having domination number greater than that of
G and is denoted by usdg(G). In this paper, we investigate
the domination uniform subdivision number of
standard graphs. Also we determine the bounds of usdg
and characterize the extremal graphs.
References
[1] Abdollah Khodkar, B. P. Mobaraky and S. M. Sheik-
holeslami, Upper Bound for the Roman Domination Subdivision
number of a Graph, AKCE J. Graphs Combin., 5 (2008),
7-14.
[2] Amitava Bhattacharya and Gurusamy Rengasamy Vi-
jayakumar, Effect of Edge-Subdivision on Vertex-Domination
in a Graph, Discussiones Mathematicae Graph Theory,
22(2002) 335-347.
[3] H. Aram, O. Favaron and S. m. Sheikholeslami, Domination
Subdivision Number of Trees, Discrete Mathematics, 309
(2009), 622-628.
[4] M. Atapour, S. M. Sheikholeslami, A. Hansberg, L. Volk-
mann and A. Khodkar, 2-Domination Subdivision Number of
Graphs, AKCE J. Graphs Combin., 5 (2008), No. 2, 165-173.
[5] Gary Chartrand, Ping Zhang, Introduction to Graph Theory
, Tata McGraw-Hill Edition, 2006.
[6] T.W. Haynes, S. M. Hedetniemi, S. T. Hedetniemi, D. P. Ja-
cobs, J. Knisely and L. C. Van der Merwe, Domination Subdivision
Numbers, Discussiones Mathematicae Graph The-
ory, 21 (2001), 239-253.
[7] J. Paulraj joseph and S. Arumugam, Domination in Subdivision
Graphs, J. Indian Math. Soc., 62(1996), 274-282.
[8] S.S.Sandhya, E. Ebin Raja Merly and B. Shiny, Subdivision
of Super GeometricMean Labeling for Quadrilateral Snake
Graphs, Int. J. Math. Trends and Tech., Vol. 24, No. 1 - Au-
gust 2015.
[9] Teresa W. Haynes, Stephen T. Hedetniemi and Peter
J. Slater, Fundamentals of Domination in Graphs, Marcel
Dekker, 1998.
[10] S. Velammal, Studies in Graph Theory: Covering, Independence,
Domination and Related Topics, Ph. D. Thesis, 1997.
Keywords
domination number, domination uniform subdivision number.