| Title:
|
Classifying trees with edge-deleted central appendage number 2 (English) |
| Author:
|
Stalder, Shubhangi |
| Author:
|
Eroh, Linda |
| Author:
|
Koker, John |
| Author:
|
Moghadam, Hosien S. |
| Author:
|
Winters, Steven J. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
99-110 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
graphs |
| Keyword:
|
trees |
| Keyword:
|
central appendage number |
| MSC:
|
05C05 |
| idZBL:
|
Zbl 1212.05068 |
| idMR:
|
MR2504694 |
| DOI:
|
10.21136/MB.2009.140644 |
| . |
| Date available:
|
2010-07-20T17:50:39Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140644 |
| . |
| Reference:
|
[1] Bielak, H.: Minimal realizations of graphs as central subgraphs.Graphs, Hypergraphs, and Matroids. Zágán, Poland (1985), 13-23. Zbl 0601.05041, MR 0848959 |
| Reference:
|
[2] Buckley, F., Miller, Z., Slater, P. J.: On graphs containing a given graph as center.J. Graph Theory 5 (1981), 427-434. Zbl 0449.05056, MR 0635706, 10.1002/jgt.3190050413 |
| Reference:
|
[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. MR 1985087 |
| Reference:
|
[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. MR 1880564 |
| Reference:
|
[5] Topp, J.: Line graphs of trees as central subgraphs.Graphs, Hypergraphs, and Matroids. Zágán, Poland (1985), 75-83. Zbl 0596.05057, MR 0848967 |
| . |
