Some results on the distance and distance signless Laplacian spectral radius of graphs and digraphs

详细信息    查看全文

• 作者：Dan Li^a ; Guoping Wang^b ; Jixiang Meng ; ^a ; ^{ldxjedu@163.com" class="auth_mail" title="E-mail the corresponding author} ; ^{mjxxju@sina.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Distance matrix ; Distance signless Laplacian matrix ; Dichromatic number ; Spectral radius
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：293
• 期：Complete
• 页码：218-225
• 全文大小：364 K

文摘

Let ρ(D(G)) denote the distance spectral radius of a graph G   and mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300316305203&_mathId=si1.gif&_user=111111111&_pii=S0096300316305203&_rdoc=1&_issn=00963003&md5=8adbdaf32505ed779e56d3298f2088da">mage" height="24" width="47" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0096300316305203-si1.gif">mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll">∂(G→)math> denote the distance signless Laplacian spectral radius of a digraph mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300316305203&_mathId=si2.gif&_user=111111111&_pii=S0096300316305203&_rdoc=1&_issn=00963003&md5=61023b8dfc262339c98b7c545670f49e">mage" height="21" width="20" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0096300316305203-si2.gif">mathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll">G→math>. Let mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300316305203&_mathId=si3.gif&_user=111111111&_pii=S0096300316305203&_rdoc=1&_issn=00963003&md5=91e2cf3405cccc399e9d628a08528171">mage" height="24" width="30" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0096300316305203-si3.gif">mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">mathvariant="script">Gn,kDmath> be the set of all k-connected graphs of order n with diameter D  . In this paper, we first determine the unique graph with minimum distance spectral radius in mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0096300316305203&_mathId=si3.gif&_user=111111111&_pii=S0096300316305203&_rdoc=1&_issn=00963003&md5=91e2cf3405cccc399e9d628a08528171">mage" height="24" width="30" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0096300316305203-si3.gif">mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">mathvariant="script">Gn,kDmath>; we then give sharp upper and lower bounds for the distance signless Laplacian spectral radius of strongly connected digraphs; we also characterize the digraphs having the maximal and minimal distance signless Laplacian spectral radii among all strongly connected digraphs; furthermore, we determine the extremal digraph with the minimal distance signless Laplacian spectral radius with given dichromatic number.