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A tricyclic graph G =(V(G), E(G)) is a connected and simple graph such that|E(G)| = |V(G)|+2. Let Tg nbe the set of all tricyclic graphs on n vertices with girth g. In this paper, we will show that there exists the unique graph which has the largest signless Laplacian spectral radius among all tricyclic graphs with girth g containing exactly three(resp., four)cycles. And at the same time, we also give an upper bound of the signless Laplacian spectral radius and the extremal graph having the largest signless Laplacian spectral radius in Tg n,where g is even. 相似文献
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The signless Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the smallest eigenvalue of its signless Laplacian matrix. In this paper, we determine the first to llth largest signless Laplacian spectral radii in the class of bicyclic graphs with n vertices. Moreover, the unique bicyclic graph with the largest or the second largest signless Laplacian spread among the class of connected bicyclic graphs of order n is determined, respectively. 相似文献
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一类树并的补图的色唯一性 总被引:10,自引:0,他引:10
彻底解决了一类不可约树并的补图是色唯一的 ,并得到了一些图的伴随多项式的最小根的重要规律 . 相似文献
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给出了ω_(4g),4h的(r_1,r_2,…,r_(4g)+4h-1)-冠的定义,讨论了ω_(4g),4h的(r_1,r_2,…,r_(4g)+4h-1)-冠的优美性,用构造性的方法给出了图ω_(4g),4h的(r_1,r_2,…,r_(4g)+4h-1)-冠的四种优美标号,并证明了这些ω_(4g),4h的(r_1,r_2,…,r_(4g)+4h-1)-冠也是交错图. 相似文献
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Let H(n; q, n1, n2, n3, n4) be a unicyclic graph with n vertices containing a cycle Cq and four hanging paths Ph1+1, Pn2+1, Pn3+1 and Pn4+1 attached at the same vertex of the cycle. In this paper, it is proved that all unicyclic graphs H (n; q, n1, n2, n3, n4) are determined by their Laplacian spectra. 相似文献