An ideal-based graph of a bounded lattice

Author:

Atani Shabaddin Ebrahimi1,Khoramdel Mehdi1ORCID,Alipour Mahsa Nikmard Rostam1

Affiliation:

1. Department of Mathematics, University of Guilan, P. O. Box 1914, Rasht, Iran

Abstract

Let [Formula: see text] be a lattice, [Formula: see text] an ideal of [Formula: see text] and [Formula: see text] the set of all elements of [Formula: see text] which are not prime to [Formula: see text]. In this paper, we investigate some interesting properties of [Formula: see text] and introduce the total graph of a lattice [Formula: see text] with respect to an ideal [Formula: see text]. It is the graph with all elements of [Formula: see text] as vertices and for distinct [Formula: see text], the vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. We investigated the basic properties of this graph and its induced subgraphs as diameter, girth, clique number, cut vertex and independence number.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

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