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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1473,
author = {Bo\v stjan Bre\v sar and Manoj Changat and Ajitha R. Subhamathi and Aleksandra Tepeh},
title = {The periphery graph of a median graph},
journal = {Discussiones Mathematicae Graph Theory},
volume = {30},
year = {2010},
pages = {17-32},
zbl = {1215.05046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1473}
}
Boštjan Brešar; Manoj Changat; Ajitha R. Subhamathi; Aleksandra Tepeh. The periphery graph of a median graph. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 17-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1473/
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