简介：图G的最大的匹配图ℳ(G)是其顶点并且在哪儿是G的最大的匹配的一张简单的图如果他们不同由，二最大的匹配在ℳ(G)是邻近的确切一个边。在这篇论文，我们证明如果一张图对它的最大的匹配图同形，那么，每块图是一个奇怪的周期。

简介：ＯＮＢＡＮＤＷＩＤＴＨＳＵＭＳＯＦＧＲＡＰＨＳＹＡＯＢＩＮＧ（姚兵）；ＷＡＮＧＪＩＡＮＦＡＮＧ（王建方）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｉｈｗｅｓｔｅｔｅｒｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ７３００７０，Ｃｈｉ...

简介：<正>ThispaperprovidesapolyhedraltheoryongraphsfromwhichthecriteriaofWhit-neyandMacLanefortheplanarityofgraphsareunified,andabriefproofoftheGausscrossingconjectureisobtained.

简介：LetGbea2-edge-connectedsimplegraph.Wegiveasufficientconditioninwhichforanyx,y∈V(G),thereisan(x,y)-trailwhichcontainseveryvertexofG(x-yisallowed)exceptsomegraphs.

简介：让G是有最大的度的一张连接的图3。我们为色彩的数字调查上面的界限<潜水艇class=“a-plus-plus”>力量图G的<啜class=“a-plus-plus”>。它被证明那\(\chi_\gamma(G)\leqslant\Delta\tfrac{{(\Delta-1)^\gamma-1}}{{\Delta-2}}+1=:M+1\)，如果并且仅当G是一张穆尔图，平等在此成立。如果G不是，一张穆尔图，和G满足下列条件之一：(1)G是非常规的，(2)尺寸g(G)21，(3)g(G)2+2，并且连接(G)3如果3，(G)4但是g(G)>6如果=2，(4)比仅仅取决于的一个给定的数字足够地大，然后(G)M1。借助于光谱半径G的毗邻矩阵的1(G)，它被看那2(G)1(G)2+1，如果并且仅当G与直径2和尺寸5是一颗星或一张穆尔图，平等在哪儿成立，并且(G)1(G)+13。

简介：A(k;g)-graphisak-regulargraphwithgirthg.A(k;g)-cageisa(k;g)-graphwiththeleastpossiblenumberofvertices.Letf(k;g)denotethenumberofverticesina(k;g)-cage.Thegirthpairofagraphgivesthelengthofashortestoddandashortestevencycle.Afc-regulargraphwithgirthpair(g,h)iscalleda(k;g,h)-graph.A(k;g,h)-cageisa(k;g,h)-graphwiththeleastpossiblenumberofvertices.Letf(k;g,h)denotethenumberofverticesina(k;g,h)-cage.Inthispaper,weprovethefollowingstrictinequalityf(k;h-1,h)

简介：Themaximummatchinggraphofagraphhasavertexforeachmaximummatchingandanedgeforeachpairofmaximummatchingswhichdifferbyexactlyoneedge.Inthispaper,weprovethattheconnectivityofmaximummatchinggraphofabipartitegraphisequaltoitsminimumdegree.

简介：Wepresentanapproachforgeneratingasortoffractalgraphsbyasimpleprobabilisticlogicneuronnetworkandshowthatthegraphscanberepresentedbyasetofcompressedcodings.Analgorithmforquicklyfindingthecodings,i.e.,recognizingthecorrespondinggraphs,isgiven.Thecodingsareshowntobeoptimal.Theresultsabovepossiblygiveustheclueforstudyingimagecompressionandpatternrecognition.

简介：一张面向的分成三部分的图是把一个方向分到一张简单的分成三部分的图的每个边的结果。为在面向的分成三部分的图D的任何顶点x(U，V，W)，让的dx+和dx？x分别地表示outdegree和indegree。定义$a_{u_i}=d_{u_i}^+-d_{u_i}^-，b_{v_j}=d_{v_j}^+-d_{v_j}^-$a_{u_i}=d_{u_i}^+-d_{u_i}^-，b_{v_j}=d_{v_j}^+-d_{v_j}^-并且$c_{w_k}=d_{w_k}^+-d_{w_k}^-$c_{w_k}=d_{w_k}^+-d_{w_k}^-作为在U，在V的vj和在W的wk的顶点ui的不平衡分别地。在这份报纸，我们获得标准让整数的序列是某面向的分成三部分的图的不平衡。

简介：InthisarticletheCn-graphsareintroduced,bywhichacharacterizationoftheembeddabilityofagraphoneitheranorientablesurfaceoranon-orientablesurfaceisprovided.

简介：ThepurposeofthispaperistodisplayanewkindofsimplegraphswhichbelongtoB.inwhichanygraphhasitsorientablegenusn,n≥3.Furthermore,foranyintegerk,1≤k≤n,thereexistsagraphB^knofB.suchthatthenon-orientablegenusofB^knisk.

简介：Abstract.LetGbeasimplegraph.ThecyclicbandwidthsumproblemistodeterminealabelingofgraphGinacyclesuchthatthetotallengthofedgesisassmallaspossible.Inthispaper,someupperandlowerboundsoncyclicbandwidthsumofgraphsarestudied.

简介：让G是顺序n的一张图并且让1，2，，n是它的特征值。Estrada索引[2]G被定义为EE=EE(G)=。在这份报纸，为EE的新界限被建立，以及在EE和图精力E之间的一些关系。

简介：ItisshownthatifGisahamiltonianbipartitegraphon2nverticesandδ(G)>2n/5+2,wheren≥60,thenGisbipancyclic.

简介：GivenadigraphD=(V;A),thecompetitiongraphGofD,denotedbyC(D),hasthesamesetofverticesasDandanedgebetweenverticesxandyifandonlyifN+D(x)\N+D(y)6=;.Inthispaper,weinvestigatethecompetitiongraphsofrounddigraphsandgiveanecessaryandsucientconditionforthesegraphstobehamiltonian.

简介：Theexponentofaprimitivedigraphhasbeengeneralizedin[2].Inthispaperweobtainnewparametersongeneralizedexponentofprimitivesimplegraphs(symmetricprimitive(0,1)matriceswithzerotrace)completely.

简介：<正>IthasbeenconjecturedthatthereisahamiltoniancycleineveryfiniteconnectedCayleygraph.Inspiteofthedifficultyinprovingthisconjecture,weshowthatalmostallCayleygraphsarehamiltonian.Thatis,astheordernofagroupGapproachesinfinity,theratioofthenumberofhamiltonianCayleygraphsofGtothetotalnumberofCayleygraphsofGapproaches1.

简介：Aheterochromatictreeisanedge-coloredtreeinwhichanytwoedgeshavedifferentcolors.Theheterochromatictreepartitionnumberofanr-edge-coloredgraphG,denotedbytr(G),istheminimumpositiveintegerpsuchthatwhenevertheedgesofthegraphGarecoloredwithrcolors,theverticesofGcanbecoveredbyatmostpvertex-disjointheterochromatictrees.Inthispaperwedeterminetheheterochromatictreepartitionnumberofr-edge-coloredcompletegraphs.Wealsofindatmosttr(Kn)vertex-disjointheterochromatictreestocoveralltheverticesinpolynomialtimeforagivenr-edge-coloringofKn.

简介：

简介：ForasimpleundirectedgraphG,denotebyA(G)the(0,1)-adjacencymatrixofG.LetthematrixS(G)=J-I-2A(G)beitsSeidelmatrix,andletSG(λ)=det(λI-S(G))beitsSeidelcharacteristicpolynomial,whereIisanidentitymatrixandJisasquarematrixallofwhoseentriesareequalto1.IfalleigenvaluesofSG(λ)areintegral,thenthegraphGiscalledS-integral.Inthispaper,ourmaingoalistoinvestigatetheeigenvaluesofSG(λ)forthecompletemultipartitegraphsG=Kn1,n2,...,nt.AnecessaryandsufficientconditionforthecompletetripartitegraphsKm,n,tandthecompletemultipartitegraphsKm,...,ms,n,...,nttobeS-integralisgiven,respectively.