کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
419953 683877 2013 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the range of size of sum graphs & integral sum graphs of a given order
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
On the range of size of sum graphs & integral sum graphs of a given order
چکیده انگلیسی

A finite simple graph GG is called a sum graph (respectively, integral sum graph) if there is a bijection  ff from the vertices of GG to a set of positive integers SS (respectively, a set of integers SS) such that uvuv is an edge of GG if and only if f(u)+f(v)∈Sf(u)+f(v)∈S. For graphs with nn vertices, we show that there exist sum graphs with mm edges if and only if m≤⌊14(n−1)2⌋ and that there exists integral sum graphs with mm edges if and only if m≤⌈38(n−1)2⌉+⌊12(n−1)⌋, except for m=⌈38(n−1)2⌉+⌊12(n−1)⌋−1 when nn is of the form 4k+14k+1. We also characterize sets of positive integers (respectively, integers) which are in bijection with sum graphs (respectively, integral sum graphs) of maximum size for a given order.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 161, Issues 16–17, November 2013, Pages 2653–2661
نویسندگان
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