Ordering trees by their distance spectral radii

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• 作者：Wenshui Lin ; Yuan Zhang ; Qi&rsquo ; an Chen ; ^{cheer@xmu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Jiwen Chen ; Chi Ma ; Junjie Chen
• 关键词：Distance spectral radii ; Transformations ; Trees ; Ordering
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：20 April 2016
• 年：2016
• 卷：203
• 期：Complete
• 页码：106-110
• 全文大小：391 K

文摘

Let mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si3.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=0c4ae2390ebfb4c83125632d8614f8b5" title="Click to view the MathML source">D(G)mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">D(G)math> be the distance matrix of a connected graph mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si4.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=2fcef41dbd80f879770bc6691124b040" title="Click to view the MathML source">GmathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll">Gmath>. The distance spectral radius of mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si4.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=2fcef41dbd80f879770bc6691124b040" title="Click to view the MathML source">GmathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll">Gmath>, denoted by mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si6.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=23c57ce0a112eea94b62d2ee60951795" title="Click to view the MathML source">∂₁(G)mathContainer hidden">mathCode"><math altimg="si6.gif" overflow="scroll">∂1(G)math>, is the largest eigenvalue of mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si3.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=0c4ae2390ebfb4c83125632d8614f8b5" title="Click to view the MathML source">D(G)mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">D(G)math>. In this paper we present a new transformation of a certain graph mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si4.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=2fcef41dbd80f879770bc6691124b040" title="Click to view the MathML source">GmathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll">Gmath> that decreases mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si6.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=23c57ce0a112eea94b62d2ee60951795" title="Click to view the MathML source">∂₁(G)mathContainer hidden">mathCode"><math altimg="si6.gif" overflow="scroll">∂1(G)math>. With the transformation, we partially confirm a conjecture proposed by Stevanović and Ilić [17] by showing that, if mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si10.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=b43bf112a57864967b522ce2d2a8c231">mage" height="21" width="60" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0166218X15004692-si10.gif">mathContainer hidden">mathCode"><math altimg="si10.gif" overflow="scroll">Δ≥⌈n2⌉math>, the double star mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si11.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=bc31f289109d9e6a6699dca0c55f0881" title="Click to view the MathML source">S_Δ,n−ΔmathContainer hidden">mathCode"><math altimg="si11.gif" overflow="scroll">SΔ,n−Δmath> uniquely minimizes the distance spectral radius among all trees on mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si12.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=6c5046192787853e3e1f8ffa552a0219" title="Click to view the MathML source">nmathContainer hidden">mathCode"><math altimg="si12.gif" overflow="scroll">nmath> vertices with maximum degree mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si13.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=844372b3216e200c3c2384f249404e81" title="Click to view the MathML source">ΔmathContainer hidden">mathCode"><math altimg="si13.gif" overflow="scroll">Δmath>. Moreover, the trees on mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004692&_mathId=si14.gif&_user=111111111&_pii=S0166218X15004692&_rdoc=1&_issn=0166218X&md5=9bcfc1b77631369e17bc44453c5490eb" title="Click to view the MathML source">n≥10mathContainer hidden">mathCode"><math altimg="si14.gif" overflow="scroll">n≥10math> vertices with the fourth and fifth least distance spectral radii are characterized.