On central-peripheral appendage numbers of uniform central graphs

Sul-Young Choi (Department of Mathematics, Statistics and Computer Science, Le Moyne College, Syracuse New York)
Jonathan Needleman (Department of Mathematics, Statistics and Computer Science, Le Moyne College, Syracuse New York)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 8, No 1 (2020): Electronic Journal of Graph Theory and Applications

In a uniform central graph (UCG) the set of eccentric vertices of a central vertex is the same for all central vertices. This collection of eccentric vertices is the centered periphery. For a pair of graphs (C,P) the central-peripheral appendage number, Aucg(C,P), is the minimum number vertices needed to be adjoined to the graphs C and P in order to construct a uniform central graph H with center V(C) and centered-periphery V(P). We compute Aucg(C,P) in terms of the radius and diameter of P and whether or not C is a complete graph. In the process we show Aucg(C, P) ≤ 6 if diam(P) > 2.   We also provide structure theorems for UCGs in terms of the centered periphery.