# The periphery graph of a median graph

• Volume: 30, Issue: 1, page 17-32
• ISSN: 2083-5892

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## Abstract

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The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are path-like median graphs with arbitrarily large geodetic number. Peripheral expansion with respect to periphery graph is also considered, and connections with the concept of crossing graph are established.

## How to cite

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Boštjan Brešar, et al. "The periphery graph of a median graph." Discussiones Mathematicae Graph Theory 30.1 (2010): 17-32. <http://eudml.org/doc/270988>.

@article{BoštjanBrešar2010,
abstract = {The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are path-like median graphs with arbitrarily large geodetic number. Peripheral expansion with respect to periphery graph is also considered, and connections with the concept of crossing graph are established.},
author = {Boštjan Brešar, Manoj Changat, Ajitha R. Subhamathi, Aleksandra Tepeh},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {median graph; Cartesian product; geodesic; periphery; peripheral expansion},
language = {eng},
number = {1},
pages = {17-32},
title = {The periphery graph of a median graph},
url = {http://eudml.org/doc/270988},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Boštjan Brešar
AU - Manoj Changat
AU - Ajitha R. Subhamathi
AU - Aleksandra Tepeh
TI - The periphery graph of a median graph
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 1
SP - 17
EP - 32
AB - The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are path-like median graphs with arbitrarily large geodetic number. Peripheral expansion with respect to periphery graph is also considered, and connections with the concept of crossing graph are established.
LA - eng
KW - median graph; Cartesian product; geodesic; periphery; peripheral expansion
UR - http://eudml.org/doc/270988
ER -

## References

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