Edge Signal Domination In Some Transformation Graphs
Keywords:
Edge Signal domination number, Line graph, Middle graph and Corona product graphAbstract
The concept of domination is an important part of graph theory. The edge signal domination is a parameter that takes into account the degree of vertices as well as the edge coverage in graphs which are crucial in the field of networking. Transformation graph is a concept in mathematics that primarily focuses on the structural change and behavior by applying graph-theoretic transformations to the graphs. It is mainly used in fields like computational modelling, biological model systems and other fields. In this article, we rely on the edge signal domination parameter and identify the parametric values for three distinct operations on graphs namely line graph, middle graph and corona product in some common graph families.
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Akiyama Jin,Hamada Takashi, Yoshimura Izumi, On Characterizations of the Middle graphs, TRU Math. 11, 35-39 (1975).
Balamurugan. S, R. Antony Doss, On the Signal Number in graphs, Discrete Mathematics, Algorithms and Applications (under review)
Balamurugan. S, R. Antony Doss, The Edge Signal Number of a graph, Discrete Mathematics, Algorithms and Applications (2020).
F Buckley, F Harary, Distance in graphs, Addison-Wesley, Longman, (1990).
Gary Chartrand, Henry Escuadro, P Zhang, Detour Distance in graphs, J. Combin. Math. Combin. Comput., 53 (2005), pp. 75-94.
Gary Chartrand, P. Zang, Introduction to Graph Theory, Tata McGraw-Hill, New Delhi, (2006).
Jachin Samuel. S, S. Angelin Kavitha Raj, On the Signal Domination Number of Graphs, Serdica Mathematical Journal, (under Review).
Jachin Samuel. S, S. Angelin Kavitha Raj, Some Results on Signal Domination Number, Indian Journal of Natural Sciences, (2024).
Jachin Samuel. S, S. Angelin Kavitha Raj, Edge Signal Domination Number of Graphs, Journal of Graph Theory, (under review).
Kathiresan. K. M, Sumathi, A Study on Signal Distance in graphs, Algebra, Graph Theory and their Application, Narosa Publishing House Pvt. Ltd, (2010), pp. 50-54.
Roberto Frucht and Frank Harary, On the corona of two graphs, Aequationes Mathematicae (1970).
Sethu Ramalingam. S and S. Balamurugan, On the signal distance in graphs, Ars Combinatoria. Accepted on (2018).
Haynes T W, Hedetniemi S T, Slater P J, Domination in Graphs: Advanced Topics, Marcel Dekker, New York, (1998).
M. Venkatachalapathy, K. Kokila, B. Abarna, Some Trends in Line Graphs, Advances in Theoretical and Applied Mathematics, vol. 11, No. 2, (2016).
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