Signed Unidominating Functions Of Corona Product Graph Cn • Km

B. Aruna; B. Maheswari

doi:https://doi.org/10.14445/22315373/IJMTT-V65I10P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 10 | Year 2019 | Article Id. IJMTT-V65I10P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I10P505

Signed Unidominating Functions Of Corona Product Graph Cn • Km

B. Aruna, B. Maheswari

Abstract

Domination in graphs is an emerging area of research in graph theory and in recent years it has been studied extensively. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et al. [5, 6]. Dominating sets have applications in diverse areas such as logistics and Communication Networks design, mobile computing, resource allocation and telecommunication etc. In Discrete Mathematics, Product of graphs occurs naturally as tools in combinatorial constructions. They give rise to an important classes of graphs and deep structural problems. Frucht and Harary [2] introduced a new product on two graphs G1 and G2, called corona product denoted by G1 • G2. In this paper, we introduced a new concept signed unidominating function and studied this concept for corona product graph Cn • Km and determined the signed unidomination and upper signed unidomination numbers for Cn • Km. Also the number of signed unidominating functions of minimum weight is found.

Keywords

Signed unidominating function, signed unidomination number, minimal signed unidominating function, upper signed unidomination number.

References

[1] Anantha Lakshmi, V. A Study on Unidominating and Total Unidominating functions of Some Standard Graphs, Ph.D. thesis, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India, (2015).
[2] Frucht, R. Harary, F On the corona of Two Graphs. AequationesMathematicae, 1970,Volume 4, Issue 3, pp. 322-325.
[3] Hedetniemi S .M, Hedetniemi, S.T. and Wimer, T. V. - Linear time resource allocation algorithms for trees. Technical report URI – 014, Department of Mathematics, Clemson University, 1987.
[4] Siva Parvathi, M. Some Studies on Dominating functions of Corona Product Graphs, Ph. D. Thesis, Sri Padmavathi Mahila Visvavidyalayam, tirupathi, Andhra Pradesh, India, 2013.
[5] T.W. Haynes, T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
[6] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 199.

Citation :

B. Aruna, B. Maheswari, "Signed Unidominating Functions Of Corona Product Graph Cn • Km," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 10, pp. 35-40, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I10P505