An algebraic characterization of geodetic graphs

Ladislav Nebeský

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 4, page 701-710
  • ISSN: 0011-4642

Abstract

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We say that a binary operation * is associated with a (finite undirected) graph G (without loops and multiple edges) if * is defined on V ( G ) and u v E ( G ) if and only if u v , u * v = v and v * u = u for any u , v V ( G ) . In the paper it is proved that a connected graph G is geodetic if and only if there exists a binary operation associated with G which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).

How to cite

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Nebeský, Ladislav. "An algebraic characterization of geodetic graphs." Czechoslovak Mathematical Journal 48.4 (1998): 701-710. <http://eudml.org/doc/30448>.

@article{Nebeský1998,
abstract = {We say that a binary operation $*$ is associated with a (finite undirected) graph $G$ (without loops and multiple edges) if $*$ is defined on $V(G)$ and $uv\in E(G)$ if and only if $u\ne v$, $u * v=v$ and $v*u=u$ for any $u$, $v\in V(G)$. In the paper it is proved that a connected graph $G$ is geodetic if and only if there exists a binary operation associated with $G$ which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).},
author = {Nebeský, Ladislav},
journal = {Czechoslovak Mathematical Journal},
keywords = {geodetic graph; binary operation; connected graph},
language = {eng},
number = {4},
pages = {701-710},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An algebraic characterization of geodetic graphs},
url = {http://eudml.org/doc/30448},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Nebeský, Ladislav
TI - An algebraic characterization of geodetic graphs
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 4
SP - 701
EP - 710
AB - We say that a binary operation $*$ is associated with a (finite undirected) graph $G$ (without loops and multiple edges) if $*$ is defined on $V(G)$ and $uv\in E(G)$ if and only if $u\ne v$, $u * v=v$ and $v*u=u$ for any $u$, $v\in V(G)$. In the paper it is proved that a connected graph $G$ is geodetic if and only if there exists a binary operation associated with $G$ which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).
LA - eng
KW - geodetic graph; binary operation; connected graph
UR - http://eudml.org/doc/30448
ER -

References

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  1. Graphs & Digraphs, Prindle, Weber & Schmidt, Boston, 1979. (1979) MR0525578
  2. Graph Theory, Addison-Wesley, Reading (Mass.), 1969. (1969) Zbl0196.27202MR0256911
  3. The Interval Function of a Graph, Mathematisch Centrum. Amsterdam, 1980. (1980) Zbl0446.05039MR0605838
  4. A characterization of the set of all shortest paths in a connected graph, Mathematica Bohemica 119 (1994), 15–20. (1994) MR1303548
  5. A characterization of geodetic graphs, Czechoslovak Math. Journal 45 (120) (1995), 491–493. (1995) MR1344515
  6. 10.1023/A:1022404624515, Czechoslovak Math. Journal 47 (122) (1997), 149–161. (1997) MR1435613DOI10.1023/A:1022404624515

Citations in EuDML Documents

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  1. Ladislav Nebeský, A tree as a finite nonempty set with a binary operation
  2. Ladislav Nebeský, New proof of a characterization of geodetic graphs
  3. Ladislav Nebeský, Travel groupoids
  4. Henry Martyn Mulder, Ladislav Nebeský, Leaps: an approach to the block structure of a graph
  5. Ladislav Nebeský, An axiomatic approach to metric properties of connected graphs
  6. Jung Rae Cho, Jeongmi Park, Yoshio Sano, Travel groupoids on infinite graphs
  7. Ladislav Nebeský, The interval function of a connected graph and a characterization of geodetic graphs

NotesEmbed ?

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