Shubhangi Stalder, Mathematics Department, University of Wisconsin Waukesha, Waukesha, WI 53188-2799, USA, e-mail: shubhangi.stalder@uwc.edu; Linda Eroh, Mathematics Department, University of Wisconsin Oshkosh, Oshkosh WI 54901-8619, USA, e-mail: eroh@uwosh.edu; John Koker, Mathematics Department, University of Wisconsin Oshkosh, Oshkosh WI 54901-8619, USA, e-mail: koker@uwosh.edu; Hosien S. Moghadam, Mathematics Department, University of Wisconsin Oshkosh, Oshkosh WI 54901-8619, USA, e-mail: moghadam@uwosh.edu; Steven J. Winters, Mathematics Department, University of Wisconsin Oshkosh, Oshkosh WI 54901-8619, USA, e-mail: winters@uwosh.edu
Abstract: The eccentricity of a vertex $v$ of a connected graph $G$ is the distance from $v$ to a vertex farthest from $v$ in $G$. The center of $G$ is the subgraph of $G$ induced by the vertices having minimum eccentricity. For a vertex $v$ in a 2-edge-connected graph $G$, the edge-deleted eccentricity of $v$ is defined to be the maximum eccentricity of $v$ in $G - e$ over all edges $e$ of $G$. The edge-deleted center of $G$ is the subgraph induced by those vertices of $G$ having minimum edge-deleted eccentricity. The edge-deleted central appendage number of a graph $G$ is the minimum difference $|V(H)| - |V(G)|$ over all graphs $H$ where the edge-deleted center of $H$ is isomorphic to $G$. In this paper, we determine the edge-deleted central appendage number of all trees.
Keywords: graphs, trees, central appendage number
Classification (MSC 2000): 05C05
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