On the Center Sets of Some Graph Classes

Abstract

For a set S of vertices and the vertex v in a connected graph G, $$\displaystyle \max _{x \in S}dx,v$$ is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set Aof vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, $$K_{m,n}$$, $$K_n-e$$, wheel graphs, odd cycles and symmetric even graphs. A graph G is called center critical if there does not a exist proper subset S of the vertex set whose S-center is the center of the graph. Here we characterize this class of graphs.