On properties of a graph that depend on its distance function
Czechoslovak Mathematical Journal (2004)
- Volume: 54, Issue: 2, page 445-456
- ISSN: 0011-4642
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topNebeský, Ladislav. "On properties of a graph that depend on its distance function." Czechoslovak Mathematical Journal 54.2 (2004): 445-456. <http://eudml.org/doc/30874>.
@article{Nebeský2004,
abstract = {If $G$ is a connected graph with distance function $d$, then by a step in $G$ is meant an ordered triple $(u, x, v)$ of vertices of $G$ such that $d(u, x) = 1$ and $d(u, v) = d(x, v) + 1$. A characterization of the set of all steps in a connected graph was published by the present author in 1997. In Section 1 of this paper, a new and shorter proof of that characterization is presented. A stronger result for a certain type of connected graphs is proved in Section 2.},
author = {Nebeský, Ladislav},
journal = {Czechoslovak Mathematical Journal},
keywords = {connected graphs; distance; steps; geodetically smooth graphs; connected graphs; distance; steps; geodetically smooth graphs},
language = {eng},
number = {2},
pages = {445-456},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On properties of a graph that depend on its distance function},
url = {http://eudml.org/doc/30874},
volume = {54},
year = {2004},
}
TY - JOUR
AU - Nebeský, Ladislav
TI - On properties of a graph that depend on its distance function
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 445
EP - 456
AB - If $G$ is a connected graph with distance function $d$, then by a step in $G$ is meant an ordered triple $(u, x, v)$ of vertices of $G$ such that $d(u, x) = 1$ and $d(u, v) = d(x, v) + 1$. A characterization of the set of all steps in a connected graph was published by the present author in 1997. In Section 1 of this paper, a new and shorter proof of that characterization is presented. A stronger result for a certain type of connected graphs is proved in Section 2.
LA - eng
KW - connected graphs; distance; steps; geodetically smooth graphs; connected graphs; distance; steps; geodetically smooth graphs
UR - http://eudml.org/doc/30874
ER -
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