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Bounds of Unique Response Strong Roman Domination
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نویسنده
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Masoumi Iman ,Mojdeh Doost Ali ,Parsian Ali
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منبع
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كنفرانس نظريه گراف و تركيبيات جبري - 2020 - دوره : 11 - یازدهمین کنفرانس بین المللی نظریه گراف و ترکیبیات جبری ایران - کد همایش: 9919164009 - صفحه:84 -87
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چکیده
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Given a simple graph g = (v; e) with maximum degree ∆. let (v0; v1; v2) be an ordered partitionof v , where vi = fv 2 v : f(v) = ig for i = 0; 1 and v2 = fv 2 v : f(v) ≥ 2g. a function f :v ! f0; 1; :::; d∆2 e + 1g is a strong roman dominating function (strdf) on g, if every v 2 v0 has aneighbor w 2 v2 and f(w) ≥ 1 + d12jn(w) v0je. a function f : v ! f0; 1; :::; d∆2 e + 1g is a uniqueresponse strong roman function (urstrf), if w 2 v0, then jn(w) v2j ≤ 1 and w 2 v1 [v2 implies thatjn(w) v2j = 0. a function f : v ! f0; 1; :::; d∆2 e + 1g is a unique response strong roman dominatingfunction (urstrdf) if it is both urstrf and strdf. the unique response strong roman dominationnumber of g, denoted by ustr(g), is the minimum weight of a unique response strong roman dominatingfunction. in this paper we initiate the study of several mathematical properties of this invariant. weobtain several bounds on such a parameter and give some realizability results for it.
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کلیدواژه
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Strong Roman Dominating Function ,Unique Response Strong Roman (Dominating) Function.
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آدرس
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University Of Tafresh, University Of Tafresh, Mathematics, Iran, University Of Mazandaran, University Of Mazandaran, Mathematics, Iran, University Of Tafresh, University Of Tafresh, Mathematics, Iran
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پست الکترونیکی
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parsian@tafreshu.ac.ir
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Authors
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