INTERSECTION GRAPH OF A SIMPLICIAL COMPLEX

Year 2013, Volume: 13 Issue: 13, 76 - 90, 01.06.2013

M. Afkhami F. Khosh-ahang

Abstract

In this note, firstly we introduce the intersection graph G(∆) of
a simplicial complex ∆, as a graph whose vertices are all facets of ∆ and two
distinct vertices are adjacent if they have non-empty intersection. We investigate
some properties of this graph and simplicial complexes. Moreover, we
apply this graph for finding a couple of upper and lower bounds for the vertex
covering number of ∆. Also, we introduce and study the intersection ideal of
a simplicial complex.

Keywords

diameter, girth, intersection graph, intersection ideal, covering number, minimal generating set, simplicial complex

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• Department of Mathematics University of Neyshabur P.O.Box 91136-899, Neyshabur, Iran e-mail: [e-mail] Fahimeh Khosh-Ahang
• Department of Mathematics Ilam University P.O.Box 69315-516, Ilam, Iran e-mail: fahime [e-mail]