Halfway Number Of Graphs
Main Article Content
Abstract
In this paper we have introduced the concept of halfway distance in graphs and the halfway number. The idea of finding the halfway distance has been developed while working with the distance parameter detour distance in graphs. The concept of halfway distance can be used to calculate the median distance in various distance locating problems. The distance found using the above concept is effective in all aspects. Let K be the set of all detour distance between every pair of vertices of G. The halfway distance is the median of K. A path of length atmost is called the halfway path. A set SV(G) is called a halfway set of G ifevery vertex of G is contained in a halfway path joining some pair of vertices of S. The halfway number is the minimum order of the halfway set and is denoted by
Article Details
References
V.G.Bhagavathi Ammal, S.Darvin Shiny, Detour Certified Domination Number of Graphs, Turkish Journal of Computer and Mathematics Education, Volume 11 No.03,2332-2344(2020).
F.Buckley et.al, Distance in Graphs(1990).
John J, Arianayagam N, The Detour Domination Number of a Graph, Discrete Mathematics Algorithms and Applications, Vol.09, No.01, (2017).
Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater, Fundamentals of Domination in Graphs, Marcel Dekkar, Inc. (1998).
Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, Inc (1998).
D.B. West, Introduction to Graph Theory, Second Edition, Prentice-Hall, Upper Saddle River, NJ(2001).