Malaysian Journal of Mathematical Sciences, September 2020, Vol. 14, No. 3
Some Results on the Graph Associated to a Lattice with Given a Filter
Malekpour, S. and Bazigaran, B.
Corresponding Email: malekpoor@grad.kashanu.ac.ir
Received date: 14 May 2019
Accepted date: 18 May 2020
Abstract:
In this paper, we study some graph-theoretical properties of \(\Gamma_{S}(L)\), a graph which the vertex set is all elements of a finite lattice \(L\) and two distinct vertices \(a\) and \(b\) are adjacent if and only if \(a\vee b \in S\), where \(S\) is a \(\wedge\)-closed subset of \(L\). As a consequence of our work, some results in Afkhami and Khashayarmanesh (2014b) are extended to the case that \(S\) is a filter.
Keywords: Clique number, chromatic number, filter, complete \(n\)-partite graph, matching number
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