کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599074 1631117 2015 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the distance spectrum of distance regular graphs
ترجمه فارسی عنوان
در طیف فاصله از نمودار های منظم فاصله
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

The distance matrix of a simple graph G   is D(G)=(dij)D(G)=(dij), where dijdij is the distance between ith and jth vertices of G. The spectrum of the distance matrix is known as the distance spectrum or D-spectrum of G. A simple connected graph G   is called distance regular if it is regular, and if for any two vertices x,y∈Gx,y∈G at distance i  , there are constant number of neighbors cici and bibi of y   at distance i−1i−1 and i+1i+1 from x respectively. In this paper we prove that distance regular graphs with diameter d   have at most d+1d+1 distinct D-eigenvalues. We find an equitable partition and the corresponding quotient matrix of the distance regular graph which gives the distinct D  -eigenvalues. We also prove that distance regular graphs satisfying bi=cd−1bi=cd−1 have at most ⌈d2⌉+2 distinct D-eigenvalues. Applying these results we find the distance spectrum of some distance regular graphs including the well known Johnson graphs. Finally we also answer the questions asked by Lin et al. [16].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 478, 1 August 2015, Pages 256–273
نویسندگان
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