# Median and quasi-median direct products of graphs

Boštjan Brešar; Pranava K. Jha; Sandi Klavžar; Blaž Zmazek

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 1-2, page 183-196
- ISSN: 2083-5892

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topBoštjan Brešar, et al. "Median and quasi-median direct products of graphs." Discussiones Mathematicae Graph Theory 25.1-2 (2005): 183-196. <http://eudml.org/doc/270212>.

@article{BoštjanBrešar2005,

abstract = {Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P₃ is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K₂ are proved, and it is shown that the only nonbipartite quasi-median direct product is K₃×K₃.},

author = {Boštjan Brešar, Pranava K. Jha, Sandi Klavžar, Blaž Zmazek},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {median graph; direct product; quasi-median graph; isometric embeddings; convexity; tree; distance},

language = {eng},

number = {1-2},

pages = {183-196},

title = {Median and quasi-median direct products of graphs},

url = {http://eudml.org/doc/270212},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Boštjan Brešar

AU - Pranava K. Jha

AU - Sandi Klavžar

AU - Blaž Zmazek

TI - Median and quasi-median direct products of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 1-2

SP - 183

EP - 196

AB - Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P₃ is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K₂ are proved, and it is shown that the only nonbipartite quasi-median direct product is K₃×K₃.

LA - eng

KW - median graph; direct product; quasi-median graph; isometric embeddings; convexity; tree; distance

UR - http://eudml.org/doc/270212

ER -

## References

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