| Title:
|
Results on $F$-continuous graphs (English) |
| Author:
|
Draganova, Anna |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
51-60 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For any nontrivial connected graph $F$ and any graph $G$, the {\it $F$-degree} of a vertex $v$ in $G$ is the number of copies of $F$ in $G$ containing $v$. $G$ is called {\it $F$-continuous} if and only if the $F$-degrees of any two adjacent vertices in $G$ differ by at most 1; $G$ is {\it $F$-regular} if the $F$-degrees of all vertices in $G$ are the same. This paper classifies all $P_4$-continuous graphs with girth greater than 3. We show that for any nontrivial connected graph $F$ other than the star $K_{1,k}$, $k \geq 1$, there exists a regular graph that is not $F$-continuous. If $F$ is 2-connected, then there exists a regular $F$-continuous graph that is not $F$-regular. (English) |
| Keyword:
|
continuous |
| Keyword:
|
$F$-continuous |
| Keyword:
|
$F$-regular |
| Keyword:
|
regular graph |
| MSC:
|
05C12 |
| MSC:
|
05C78 |
| idZBL:
|
Zbl 1224.05434 |
| idMR:
|
MR2486615 |
| . |
| Date available:
|
2010-07-20T14:50:52Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140463 |
| . |
| Reference:
|
[1] Chartrand, G., Eroh, L., Schultz, M., Zhang, P.: An introduction to analytic graph theory.Util. Math. 59 (2001), 31-55. Zbl 0989.05035, MR 1832600 |
| Reference:
|
[2] Chartrand, G., Holbert, K. S., Oellermann, O. R., Swart, H. C.: $F$-Degrees in graphs.Ars Comb. 24 (1987), 133-148. Zbl 0643.05055, MR 0917968 |
| Reference:
|
[3] Chartrand, G., Jarrett, E., Saba, F., Salehi, E., Zhang, P.: $F$-Continuous graphs.Czech. Math. J. 51 (2001), 351-361. Zbl 0977.05042, MR 1844315, 10.1023/A:1013751031651 |
| Reference:
|
[4] Erdös, P., Sachs, H.: Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl.Wiss Z. Martin-Luther-Univ. Halle-Wittenberg, Math.-Naturwiss. Reihe 12 (1963), 251-258 . MR 0165515 |
| Reference:
|
[5] Gimbel, J., Zhang, P.: Degree-continuous graphs.Czech. Math. J. 51 (2001), 163-171. Zbl 1079.05504, MR 1814641 |
| . |
