Classifying trees with edge-deleted central appendage number 2

Shubhangi Stalder; Linda Eroh; John Koker; Hosien S. Moghadam; Steven J. Winters

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 1, page 99-110
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Stalder, Shubhangi, et al. "Classifying trees with edge-deleted central appendage number 2." Mathematica Bohemica 134.1 (2009): 99-110. <http://eudml.org/doc/38077>.

@article{Stalder2009,
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.},
author = {Stalder, Shubhangi, Eroh, Linda, Koker, John, Moghadam, Hosien S., Winters, Steven J.},
journal = {Mathematica Bohemica},
keywords = {graphs; trees; central appendage number; graphs; trees; central appendage number},
language = {eng},
number = {1},
pages = {99-110},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Classifying trees with edge-deleted central appendage number 2},
url = {http://eudml.org/doc/38077},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Stalder, Shubhangi
AU - Eroh, Linda
AU - Koker, John
AU - Moghadam, Hosien S.
AU - Winters, Steven J.
TI - Classifying trees with edge-deleted central appendage number 2
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 1
SP - 99
EP - 110
AB - 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.
LA - eng
KW - graphs; trees; central appendage number; graphs; trees; central appendage number
UR - http://eudml.org/doc/38077
ER -

References

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  1. Bielak, H., Minimal realizations of graphs as central subgraphs, Graphs, Hypergraphs, and Matroids. Zágán, Poland (1985), 13-23. (1985) Zbl0601.05041MR0848959
  2. Buckley, F., Miller, Z., Slater, P. J., 10.1002/jgt.3190050413, J. Graph Theory 5 (1981), 427-434. (1981) Zbl0449.05056MR0635706DOI10.1002/jgt.3190050413
  3. Koker, J., McDougal, K., Winters, S. J., The edge-deleted center of a graph, Proceedings of the Eighth Quadrennial Conference on Graph Theory, Combinatorics, Algorithms and Applications. 2 (1998), 567-575. (1998) MR1985087
  4. Koker, J., Moghadam, H., Stalder, S., Winters, S. J., The edge-deleted central appendage number of graphs, Bull. Inst. Comb. Appl. 34 (2002), 45-54. (2002) MR1880564
  5. Topp, J., Line graphs of trees as central subgraphs, Graphs, Hypergraphs, and Matroids. Zágán, Poland (1985), 75-83. (1985) Zbl0596.05057MR0848967

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