Domination in Double Vertex Graphs

Roopa Prabhu, K. Manjula

Abstract


In this paper many bounds for the domination number of double vertex graph and its complement are obtained. Further we have obtained some characterizations of domination number of double vertex graph.


Keywords


Double vertex graph; Minimal dominating set; Domination number

Full Text:

PDF

References


Y. Alavi, D. R. Lick and J. Liu, Hamiltonian properties of graphs and double vertex graphs, Congressus Numerantium 104 (1994), 33 – 44.

Y. Alavi, D. R. Lick and J. Liu, Survey of double vertex graphs, Graphs and Combinatorics 18(4) (2002), 709 – 715, DOI: 10.1007/s003730200055.

G. Chartrand and P. Zhang, Introduction to Graph Theory, Tata McGraw-Hill, New Delhi (2006).

J. Jacob, W. Goddard and R. Laskar, Double vertex graphs and complete double vertex graphs, Congressus Numerantium 188 (2007), 161 – 174.

T. W. Haynes, S. T. Heidetniemi and P. J. Slater, Fundamentals of Domination in Graphs, CRC Press (1998).

Y. B. Maralabhavi, Anupama S. B. and Venkanagouda M. Goudar, Domination number of jump graph, International Mathematical Forum 8(16) (2013), 753 – 758, DOI: 10.12988/imf.2013.13079.

M. H. Muddebihal and D. Basavarajappa, Independent domination in line graphs, International Journal of Scientific & Engineering Research 3(6) (2012), 1 – 5.

V. G. Vizing, The Cartesian product of graphs, Vycisl. Sistemy 9 (1963), 30 – 43.




DOI: http://dx.doi.org/10.26713%2Fjims.v11i3-4.1308

eISSN 0975-5748; pISSN 0974-875X