Split Domination Number in Vertex Semi-Middle Graph

Venkanagouda M Goudar; Rajendra Prasad K C; Niranjan K M

doi:https://doi.org/10.14445/22315373/IJMTT-V68I4P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 4 | Year 2022 | Article Id. IJMTT-V68I4P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I4P504

Split Domination Number in Vertex Semi-Middle Graph

Venkanagouda M Goudar, Rajendra Prasad K C, Niranjan K M

Received	Revised	Accepted
06 Mar 2022	07 Apr 2023	18 Apr 2022

Abstract

Let 𝐺(𝑝,𝑞) be a connected graph and 𝑀𝑣(𝐺) be its corresponding vertex semi middle graph. A dominating set 𝐷⊆𝑉[𝑀𝑣(𝐺)] is split dominating set 〈𝑉[𝑀𝑣(𝐺)]−𝐷〉 is disconnected. The minimum size of D is called the split domination number of 𝑀𝑣(𝐺) and is denoted by 𝛾𝑠[𝑀𝑣(𝐺)] . In this paper we obtain several results on split domination number.

Keywords

Domination number, Split domination number, Vertex semi-middle graph.

References

[1] Harary, F., Graph Theory, Addison-Wesley Reading Mass, (1969), p.72, 107.
[2] Haynes, T.W. Hedetniemi, S.T. and Slater, P.J., Fundamentals of Domination in Graphs, Marcel Dekker: New York, (1997).
[3] Haynes, T.W. Hedetniemi, S.T. and Slater, P.J., Domination in Graphs: Advanced Topics, Marcel Dekker: New York, (1998).
[4] Kulli, V R., B.Janakiram, Niranjan, K M., The dominating graph. Graph Theory Notes of New York, 46 (2004) 5-8.
[5] Kulli, V R. Janakiram, B, Niranjan, K M, The vertex minimal dominating graph, Acta Ciencia Indica. Mathematics, 28(3) (2002) 435-440
[6] Kulli, V.R. and Janakiram, B., The Split Domination Number of Graph, Graph Theory Notes of New York, New York Academy of Sciences, XXXII (1997) 16-19.
[7] Kulli V.R, Niranjan K.M., The Semi-Splitting Block Graph of A Graph, Journal of Scientific Research, 2(3) (2010) 485-488.
[8] Kulli V.R, Basavanagouda B, Niranjan K.M., Quasi-Total Graphs With Crossing Numbers, Journal of Scientific Research, 2(2) (2010) 257-263.
[9] Kulli V.R., Niranjan K.M., On Minimally Nonouterplanarity of The Semi-Total (Point) Graph of A Graph, J. Sci. Res., 1(3) (2009) 551-557.
[10] Kulli V.R., Niranjan K.M., The Total Closed Neighbourhood Graphs with Crossing Number Three and Four, Journal of Analysis and Computation, 1(1) (2005) 47- 56.
[11] Maralabhavi, Y.B. Venkanagouda M. Goudar and Anupama, S.B., Some Domination Parameters on Jump Graph, International Journal of Pure and Applied Mathematics, 113 (2017) 47-55.
[12] Maralabhavi, Y.B. Anupama, S.B. and Venkanagouda M. Goudar, Domination Number of Jump Graph, International Mathematical Forum, Hikari Publishing Ltd, 8 (2013) 753-758.
[13] Niranjan K M, Rajendra Prasad K C, Venkanagouda M Goudar, Dupadahalli Basavaraja, Forbidden Subgraphs for Planar Vertex Semi-Middle Graph, JNNCE Journal of Engineering and Management, 5(2) (2022) 44-47.
[14] Niranjan K. M., Radha R. Iyer, Biradar M. S., Dupadahalli Basavaraja, The Semi-Splitting Block Graphs with Crossing Numbers Three and Forbidden Subgraphs for Crossing Number One, Asian Journal of Current Research, 5(1) (2020) 25-32.
[15] Niranjan K.M., Forbidden Subgraphs for Planar and Outerplanar Interms of Blict Graphs, Journal of Analysis and Computation, 2(1) (2006) 19-22.
[16] Niranjan K.M., Nagaraja P., Lokesh V., Semi-Image Neighborhood Block Graphs with Crossing Numbers, Journal of Scientific Research, 5(4) (2013) 295-299.
[17] Rajendra Prasad KC, Venkanagouda M. Goudar and Niranjan KM, Pathos Vertex Semi-Middle Graph of a Tree, South East Asian J. of Mathematics and Mathematical Sciences, 16(1), (2020) 171-176.
[18] Rajendra Prasad K C, Venkanagouda M. Goudar and K.M. Niranjan, Pathos Edge Semi-Middle Graph of a Tree, Malaya Journal of Matematik, 8(4) (2020) 2190-2193.
[19] Rajendra Prasad, K.C. Niranjan, K.M. and Venkanagouda M. Goudar, Vertex Semi-Middle Graph of a Graph, Malaya Journal of Matematik, 7 (2019) 786-789
[20] ra Prasad, K.C. Niranjan, K.M. and Venkanagouda M. Goudar, Vertex Semi-Middle Domination in Graphs, Jour of Adv Research in Dynamical and Control Systems, 12 (2020) 83-89.
[21] enkanagouda M. Goudar, Pathos Vertex Semientire Graph of a Tree, International Journal of Applied Mathematical Research, 1(4) (2012) 666-670.
[22] Venkanagouda M. Goudar, K. S. Ashalatha, Venkatesha, M. H. Muddebihal, On the Geodetic Number of Line Graph, Int. J. Contemp. Math. Sciences, 7(46) (2012) 2289 – 2295

Citation :

Venkanagouda M Goudar, Rajendra Prasad K C, Niranjan K M, "Split Domination Number in Vertex Semi-Middle Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 4, pp. 18-22, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I4P504