On properties of a graph that depend on its distance function

Ladislav Nebeský

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 2, page 445-456
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Nebeský, 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 -

References

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  6. 10.1023/A:1022404624515, Czechoslovak Math.  J. 47 (122) (1997), 149–161. (1997) MR1435613DOI10.1023/A:1022404624515
  7. 10.1023/A:1022472700080, Czechoslovak Math.  J. 50 (125) (2000), 3–14. (2000) MR1745453DOI10.1023/A:1022472700080
  8. 10.1023/A:1022401506441, Czechoslovak Math.  J. 50 (125) (2000), 121–133. (2000) MR1745467DOI10.1023/A:1022401506441
  9. A tree as a finite nonempty set with a binary operation, Math. Bohem. 125 (2000), 455–458. (2000) MR1802293

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