An Application Of Max-Radial Number Of Graphs In Game Theory

Document Type : Primary Research paper


1 Department of Mathematics Sri Vidhya College of Arts and Science Virudhunagar, India

2 Research Department of Mathematics VHN Senthi kumara Nadar college Virudhunagar, India


For a graph 𝑮(𝑽,𝑬), the 𝑺-radial set, 𝑩𝑹(𝑺), is defined for any set 𝑺⊆𝑽, as the set of vertices 𝒖∈𝑽\𝑺 which are at a distance of radius of 𝑮 from some vertex 𝒗∈𝑺. The Max-Radial number of 𝑮 is the parameter which is defined as {|𝑩𝑹(𝑺)|−|𝑺|𝑺 𝒎𝒂𝒙}. The study on this parameter faces the challenge of placing the maximum number of maximal length strings with certain conditions in any graph model. In this paper, we study the varied properties of this parameter. We characterize the extremal graphs for the Max-Radial concept in graphs. Also we prove the existence of graphs with given order and Max-Radial number.