کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
418926 681727 2015 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
General Randić matrix and general Randić incidence matrix
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
General Randić matrix and general Randić incidence matrix
چکیده انگلیسی

Let GG be a connected graph with vertex set V(G)={v1,…,vn}V(G)={v1,…,vn} and edge set E(G)={e1,…,em}E(G)={e1,…,em}. Let didi be the degree of the vertex vivi. The general Randić matrix Rα=((Rα)ij)n×n of GG is defined by (Rα)ij=(didj)α if vertices vivi and vjvj are adjacent in GG and 0 otherwise. The Randić signless Laplacian matrix Qα=D2α+1+Rα, where αα is a nonzero real number and DD is the degree diagonal matrix of GG. The general Randić energy REαREα is the sum of absolute values of the eigenvalues of Rα. The general Randić incidence matrix BRα=((BRα)ij)n×mBRα=((BRα)ij)n×m of a graph GG is defined by (BRα)ij=diα if vivi is incident to ejej and 0 otherwise. Naturally, the general Randić incidence energy BEαBEα is the sum of the singular values of BRαBRα. In this paper, we investigate the connected graphs with ss distinct Rα-eigenvalues, where 2≤s≤n2≤s≤n. Moreover, we establish the relation between the Randić signless Laplacian eigenvalues of GG and the general Randić energy of its subdivided graph S(G)S(G). Also we give lower and upper bounds on the general Randić incidence energy. Finally, the general Randić incidence energy of a graph and that of its subgraphs are compared.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 186, 11 May 2015, Pages 168–175
نویسندگان
, ,