Geodesic
$F$-continuous graphs
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 351-361.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 05C12, 05C38, 05C40, 05C75
Keywords: $F$-degree; $F$-degree continuous 
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     author = {Chartrand, Gary and Jarrett, Elzbieta B. and Saba, Farrokh and Salehi, Ebrahim and Zhang, Ping},
     title = {$F$-continuous graphs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {351--361},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {2001},
     mrnumber = {1844315},
     zbl = {0977.05042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2001__51_2_a9/}
}
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Chartrand, Gary; Jarrett, Elzbieta B.; Saba, Farrokh; Salehi, Ebrahim; Zhang, Ping. $F$-continuous graphs. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 351-361. http://geodesic.mathdoc.fr/item/CMJ_2001__51_2_a9/