کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897728 | 1631040 | 2018 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An upper bound of the nullity of a graph in terms of order and maximum degree
ترجمه فارسی عنوان
مرز بالایی از نادیده گرفتن یک گراف در ترتیب و حداکثر درجه
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let G be a finite undirected graph without loops and multiple edges. By η,Î and n we respectively denote the nullity, the maximum vertex degree and the order of G. In [10], it was proved that ηâ¤nâ2ânâ1Îâ when G is a tree. This result was generalized to a bipartite graph by [25]. For a reduced bipartite graph G, the above inequality was improved to nâ2â2ln2Î by [27]. However, the problem of bounding the nullity of an arbitrary graph G in terms of n and Î is left open for more than ten years. In this article, we aim to solve such a left problem. We prove that ηâ¤Îâ1În for an arbitrary graph G with order n and maximum degree Î, and the equality holds if and only if G is the disjoint union of some copies of KÎ,Î.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 555, 15 October 2018, Pages 314-320
Journal: Linear Algebra and its Applications - Volume 555, 15 October 2018, Pages 314-320
نویسندگان
Qi Zhou, Dein Wong, Dongqin Sun,