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A NOTE ON THE EXTENDED TOTAL GRAPH OF COMMUTATIVE RINGS
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نویسنده
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esmaeili khalil saraei f. ,navidinia e.
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منبع
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journal of algebra and related topics - 2018 - دوره : 6 - شماره : 1 - صفحه:25 -33
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چکیده
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Let r be a commutative ring and h a nonempty proper subset of r. in this paper, the extended total graph, denoted by eth(r) is presented, where h is a multiplicative-prime subset of r. it is the graph with all elements of r as vertices, and for distinct p, q ∈ r, the vertices p and q are adjacent if and only if rp+sq ∈ h for some r, s ∈ rh. we also study the two (induced) subgraphs eth(h) and eth(r h), with vertices h and r h, respectively. among other things, the diameter and the girth of eth(r) are also studied.
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کلیدواژه
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Total graph ,prime ideal ,multiplicative-prime subset
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آدرس
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university of tehran, fouman faculty of engineering, college of engineering, Iran, university of guilan, faculty of mathematical sciences, department of mathematics, Iran
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پست الکترونیکی
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elnaz.navidinia@yahoo.com
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Authors
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