# An algebraic characterization of geodetic graphs

Czechoslovak Mathematical Journal (1998)

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

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topNebeský, 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

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

## Citations in EuDML Documents

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

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