| Title:
|
$F$-continuous graphs (English) |
| Author:
|
Chartrand, Gary |
| Author:
|
Jarrett, Elzbieta B. |
| Author:
|
Saba, Farrokh |
| Author:
|
Salehi, Ebrahim |
| Author:
|
Zhang, Ping |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
351-361 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a nontrivial connected graph $F$, the $F$-degree of a vertex $v$ in a graph $G$ is the number of copies of $F$ in $G$ containing $v$. A graph $G$ is $F$-continuous (or $F$-degree continuous) if the $F$-degrees of every two adjacent vertices of $G$ differ by at most 1. All $P_3$-continuous graphs are determined. It is observed that if $G$ is a nontrivial connected graph that is $F$-continuous for all nontrivial connected graphs $F$, then either $G$ is regular or $G$ is a path. In the case of a 2-connected graph $F$, however, there always exists a regular graph that is not $F$-continuous. It is also shown that for every graph $H$ and every 2-connected graph $F$, there exists an $F$-continuous graph $G$ containing $H$ as an induced subgraph. (English) |
| Keyword:
|
$F$-degree |
| Keyword:
|
$F$-degree continuous |
| MSC:
|
05C12 |
| MSC:
|
05C38 |
| MSC:
|
05C40 |
| MSC:
|
05C75 |
| idZBL:
|
Zbl 0977.05042 |
| idMR:
|
MR1844315 |
| . |
| Date available:
|
2009-09-24T10:43:04Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127652 |
| . |
| Reference:
|
[1] G. Chartrand, L. Eroh, M. Schultz and P. Zhang: An introduction to analytic graph theory.Utilitas Math (to appear). MR 1832600 |
| Reference:
|
[2] G. Chartrand, K. S. Holbert, O. R. Oellermann and H. C. Swart: $F$-degrees in graphs.Ars Combin. 24 (1987), 133–148. MR 0917968 |
| Reference:
|
[3] G. Chartrand and L. Lesniak: Graphs $\&$ Digraphs (third edition).Chapman $\&$ Hall, New York, 1996. MR 1408678 |
| Reference:
|
[4] P. Erdös and H. Sachs: Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl.Wiss Z. Univ. Halle, Math-Nat. 12 (1963), 251–258. MR 0165515 |
| Reference:
|
[5] J. Gimbel and P. Zhang: Degree-continuous graphs.Czechoslovak Math. J (to appear). MR 1814641 |
| Reference:
|
[6] D. König: Über Graphen und ihre Anwendung auf Determinantheorie und Mengenlehre.Math. Ann. 77 (1916), 453–465. MR 1511872, 10.1007/BF01456961 |
| . |
