کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900940 | 1631724 | 2018 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Solution to a conjecture on a Nordhaus-Gaddum type result for the Kirchhoff index
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
Let G be a connected graph. The resistance distance between any two vertices of G is defined as the net effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index of G, denoted by Kf(G), is the sum of resistance distances between all pairs of vertices in G. In [28], it was conjectured that for a connected n-vertex graph G with a connected complement G¯,Kf(G)+Kf(G¯)â¤n3ân6+nâk=1nâ11nâ4sin2kÏ2n,with equality if and only if G or G¯ is the path graph Pn. In this paper, by employing combinatorial and electrical techniques, we show that the conjecture is true except for a complementary pair of small graphs on five vertices.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 332, 1 September 2018, Pages 241-249
Journal: Applied Mathematics and Computation - Volume 332, 1 September 2018, Pages 241-249
نویسندگان
Yujun Yang, Yuliang Cao, Haiyuan Yao, Jing Li,