کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6423514 1342400 2012 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Average distance in weighted graphs
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Average distance in weighted graphs
چکیده انگلیسی

We consider the following generalisation of the average distance of a graph. Let G be a connected, finite graph with a nonnegative vertex weight function c. Let N be the total weight of the vertices. If N≠0,1, then the weighted average distance of G with respect to c is defined by μc(G)=N2−1∑{u,v}⊆Vc(u)c(v)dG(u,v), where dG(u,v) denotes the usual distance between u and v in G. If c(v)=1 for all vertices v of G, then μc(G) is the ordinary average distance.We present sharp bounds on μc for trees, cycles, and graphs with minimum degree at least 2. We show that some known results for the ordinary average distance also hold for the weighted average distance, provided that each vertex has weight at least 1.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 312, Issue 1, 6 January 2012, Pages 12-20
نویسندگان
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