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Chromatic number an...
Chromatic number and clique number of subgraphs of regular graph of matrix algebras
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- Akbari, Saieed (author)
- Sharif Univ Technol, Dept Math Sci, Tehran, Iran
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- Aryapoor, Masood, 1977- (author)
- Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran,MAM
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- Jamaali, M. (author)
- Sharif Univ Technol, Dept Math Sci, Tehran, Iran
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(creator_code:org_t)
- Elsevier BV, 2012
- 2012
- English.
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In: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 436:7, s. 2419-2424
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Abstract
Subject headings
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- Let R be a ring and X subset of R be a non-empty set. The regular graph of X, Gamma(X), is defined to be the graph with regular elements of X (non-zero divisors of X) as the set of vertices and two vertices are adjacent if their sum is a zero divisor. There is an interesting question posed in BCC22. For a field F, is the chromatic number of Gamma(GL(n)(F)) finite? In this paper, we show that if G is a soluble sub-group of GL(n)(F), then x (Gamma(G)) < infinity. Also, we show that for every field F, chi (Gamma(M-n(F))) = chi (Gamma(M-n(F(x)))), where x is an indeterminate. Finally, for every algebraically closed field F, we determine the maximum value of the clique number of Gamma(< A >), where < A > denotes the subgroup generated by A is an element of GL(n)(F). (C) 2011 Elsevier Inc. All rights reserved.
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
Keyword
- Chromatic number
- Clique number
- Determinant
- Regular graph
Publication and Content Type
- ref (subject category)
- art (subject category)
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