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Article: Beck's graphs associated with [Z.sub.n] and their characteristic polynomials.
- Article from:
- International Journal of Applied Mathematics & Statistics
- Article date:
- November 1, 2007
- Author:
CopyrightCOPYRIGHT 2007 Centre for Environment, Social, and Economic Research. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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ABSTRACT
In this paper, the graphs G([Z.sub.n]) associated with the residue class rings [Z.sub.n] defined by I. Beck (?) where the vertices set [Z.sub.n] and the edges set such that an edge [a, b] if and only if ab = 0 for two distinct vertices a, b in [Z.sub.n]. Let An be an adjacent matrix of a graph G([Z.sub.n]). When the chromatic number of G([Z.sub.n]) is three we consider the characteristic polynomial of An and the number of distinct 4-cycles of G([Z.sub.n]). Also, we give some examples of Beck's graphs associated with [R.sub.n,m] = [Z.sub.n][x] = [Z.sub.n][X]/([X.sup.m]).
Keywords: Beck's graphs, characteristic polynomials, Adjacent matrix, ring, ...