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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Solution to a conjecture on a Nordhaus-Gaddum type result for the Kirchhoff index
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¯)≤n3−n6+n∑k=1n−11n−4sin2kπ2n,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
نویسندگان
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