کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900578 | 1631718 | 2018 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Graphs preserving Wiener index upon vertex removal
ترجمه فارسی عنوان
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
The Wiener index W(G) of a connected graph G is defined as the sum of distances between all pairs of vertices in G. In 1991, Å oltés posed the problem of finding all graphs G such that the equality W(G)=W(Gâv) holds for all their vertices v. Up to now, the only known graph with this property is the cycle C11. Our main object of study is a relaxed version of this problem: Find graphs for which Wiener index does not change when a particular vertex v is removed. In an earlier paper we have shown that there are infinitely many graphs with the vertex v of degree 2 satisfying this property. In this paper we focus on removing a higher degree vertex and we show that for any kâ¯â¥â¯3 there are infinitely many graphs with a vertex v of degree k satisfying W(G)=W(Gâv). In addition, we solve an analogous problem if the degree of v is nâ1 or nâ2. Furthermore, we prove that dense graphs cannot be a solutions of Å oltes's problem. We conclude that the relaxed version of Å oltés's problem is rich with a solutions and we hope that this can provide an insight into the original problem of Å oltés.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 338, 1 December 2018, Pages 25-32
Journal: Applied Mathematics and Computation - Volume 338, 1 December 2018, Pages 25-32
نویسندگان
Martin Knor, Snježana MajstoroviÄ, Riste Å krekovski,