Results on -continuous graphs
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 1, page 51-60
- ISSN: 0011-4642
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topDraganova, Anna. "Results on $F$-continuous graphs." Czechoslovak Mathematical Journal 59.1 (2009): 51-60. <http://eudml.org/doc/37907>.
@article{Draganova2009,
abstract = {For any nontrivial connected graph $F$ and any graph $G$, the $F$-degree of a vertex $v$ in $G$ is the number of copies of $F$ in $G$ containing $v$. $G$ is called $F$-continuous if and only if the $F$-degrees of any two adjacent vertices in $G$ differ by at most 1; $G$ is $F$-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 $K_\{1,k\}$, $k \ge 1$, 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.},
author = {Draganova, Anna},
journal = {Czechoslovak Mathematical Journal},
keywords = {continuous; $F$-continuous; $F$-regular; regular graph; continuous graphs; -continuous graphs; -regular graphs; regular graphs},
language = {eng},
number = {1},
pages = {51-60},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Results on $F$-continuous graphs},
url = {http://eudml.org/doc/37907},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Draganova, Anna
TI - Results on $F$-continuous graphs
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 51
EP - 60
AB - For any nontrivial connected graph $F$ and any graph $G$, the $F$-degree of a vertex $v$ in $G$ is the number of copies of $F$ in $G$ containing $v$. $G$ is called $F$-continuous if and only if the $F$-degrees of any two adjacent vertices in $G$ differ by at most 1; $G$ is $F$-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 $K_{1,k}$, $k \ge 1$, 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.
LA - eng
KW - continuous; $F$-continuous; $F$-regular; regular graph; continuous graphs; -continuous graphs; -regular graphs; regular graphs
UR - http://eudml.org/doc/37907
ER -
References
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