کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
420348 683925 2010 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bounds on the index of the signless Laplacian of a graph
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
Bounds on the index of the signless Laplacian of a graph
چکیده انگلیسی

Let G=(V,E)G=(V,E) be a simple, undirected graph of order nn and size mm with vertex set VV, edge set EE, adjacency matrix AA and vertex degrees Δ=d1≥d2≥⋯≥dn=δΔ=d1≥d2≥⋯≥dn=δ. The average degree of the neighbor of vertex vivi is mi=1di∑j=1naijdj. Let DD be the diagonal matrix of degrees of GG. Then L(G)=D(G)−A(G)L(G)=D(G)−A(G) is the Laplacian matrix of GG and Q(G)=D(G)+A(G)Q(G)=D(G)+A(G) the signless Laplacian matrix of GG. Let μ1(G)μ1(G) denote the index of L(G)L(G) and q1(G)q1(G) the index of Q(G)Q(G). We survey upper bounds on μ1(G)μ1(G) and q1(G)q1(G) given in terms of the didi and mimi, as well as the numbers of common neighbors of pairs of vertices. It is well known that μ1(G)≤q1(G)μ1(G)≤q1(G). We show that many but not all upper bounds on μ1(G)μ1(G) are still valid for q1(G)q1(G).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 158, Issue 4, 28 February 2010, Pages 355–360
نویسندگان
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