Geodesic
Classifying trees with edge-deleted central appendage number 2
Mathematica Bohemica, Tome 134 (2009) no. 1, pp. 99-110

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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.
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.
DOI : 10.21136/MB.2009.140644
Classification : 05C05
Keywords: graphs; trees; central appendage number 
Stalder, Shubhangi; Eroh, Linda; Koker, John; Moghadam, Hosien S.; Winters, Steven J. Classifying trees with edge-deleted central appendage number 2. Mathematica Bohemica, Tome 134 (2009) no. 1, pp. 99-110. doi: 10.21136/MB.2009.140644
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