کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6420183 1631785 2015 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An inequality between the edge-Wiener index and the Wiener index of a graph
ترجمه فارسی عنوان
یک نابرابری بین شاخص لبه-وینر و شاخص وینر یک گراف
کلمات کلیدی
شاخص وینر، شاخص گوتمن، نمودار خط،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی

The Wiener index W(G) of a connected graph G is defined to be the sum ∑u, vd(u, v) of distances between all unordered pairs of vertices in G. Similarly, the edge-Wiener index We(G) of G is defined to be the sum ∑e, fd(e, f) of distances between all unordered pairs of edges in G, or equivalently, the Wiener index of the line graph L(G). Wu (2010) showed that We(G) ≥ W(G) for graphs of minimum degree 2, where equality holds only when G is a cycle. Similarly, in Knor et al. (2014), it was shown that We(G)≥δ2−14W(G) where δ denotes the minimum degree in G. In this paper, we extend/improve these two results by showing that We(G)≥δ24W(G) with equality satisfied only if G is a path on 3 vertices or a cycle. Besides this, we also consider the upper bound for We(G) as well as the ratio We(G)W(G). We show that among graphs G on n vertices We(G)W(G) attains its minimum for the star.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 269, 15 October 2015, Pages 714-721
نویسندگان
, , ,