Title of article :
On the Total Monophonic Number of a Graph
Author/Authors :
Arumugam ، Subramanian National Centre for Advanced Research in Discrete Mathematics - Kalasalingam Academy of Research and Education Kalasalingam University Anand Nagar , Santhakumaran ، A.P. Department of Mathematics - Hindustan Institute of Technology and Science Hindustan Institute of Technology and Science Chennai - 603 103 , Titus ، P. Department of Mathematics - University College of Engineering Nagercoil - Anna University , Ganesamoorthy ، K. Department of Mathematics - Coimbatore Institute of Technology (Government Aided Autonomous Institution) Coimbatore - 641 014 , Murugan ، M. Department of Mathematics - Coimbatore Institute of Technology
Abstract :
Let G = (V, E) be a connected graph of order n. A path P in G which does not have a chord is called a monophonic path. A subset S of V is called a monophonic set if every vertex v in V lies in a x-y monophonic path where x, y ∈ S. If further the induced subgraph G[S] has no isolated vertices, then S is called a total monophonic set. The total monophonic number mt(G) and the upper total monophonic number m^+ t (G) are respectively the minimum cardinality of a total monophonic set and the maximum cardinality of a minimal total monophonic set. In this paper we determine the value of these parameters for some classes of graphs and establish bounds for the same. We also prove the existence of graphs with prescribed values for mt(G) and m^+ t (G).
Keywords :
total geodetic set , total monophonic set , total monophonic number , min , imal total monophonic set , upper total monophonic number
Journal title :
Communications in Combinatorics and Optimization
Journal title :
Communications in Combinatorics and Optimization
