### On central-peripheral appendage numbers of uniform central graphs

#### Abstract

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, *A*_{ucg}(*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 *A*_{ucg}(*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 *A*_{ucg}(*C*, *P*) ≤ 6 if diam(*P*) > 2. We also provide structure theorems for UCGs in terms of the centered periphery.

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PDFDOI: http://dx.doi.org/10.5614/ejgta.2020.8.1.12

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