کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416366 | 1631129 | 2015 | 8 صفحه PDF | دانلود رایگان |
Richard Brualdi proposed in StevaniviÄ (2007) [10] the following problem:(Problem AWGS.4) Let Gn and Gnâ² be two nonisomorphic graphs on n vertices with spectraλ1â¥Î»2â¥â¯â¥Î»nandλ1â²â¥Î»2â²â¥â¯â¥Î»nâ², respectively. Define the distance between the spectra of Gn and Gnâ² asλ(Gn,Gnâ²)=âi=1n(λiâλiâ²)2(or use âi=1n|λiâλiâ²|). Define the cospectrality of Gn bycs(Gn)=minâ¡{λ(Gn,Gnâ²):Gnâ² not isomorphic to Gn}. Letcsn=maxâ¡{cs(Gn):Gn a graph on n vertices}. Problem AInvestigate cs(Gn) for special classes of graphs.Problem BFind a good upper bound on csn.In this paper we completely answer Problem B by proving that csn=2 for all nâ¥2, whenever csn is computed with respect to any âp-norm with 1â¤p<â and csn=1 with respect to the ââ-norm. The cospectrality cs(Km,n) of the complete bipartite graph Km,n for all positive integers m and n with mâ¤n
Journal: Linear Algebra and its Applications - Volume 466, 1 February 2015, Pages 401-408