ON THE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF UNICYCLIC GRAPHS WITH FIXED MATCHING NUMBER

Jing-Ming Zhang, Ting Huang, Ji-Ming Guo
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引用次数: 3

Abstract

We determine the graph with the largest signless Laplacian spec- tral radius among all unicyclic graphs with fixed matching number. respectively. The largest eigenvalues of A(G) and Q(G) are called the spectral radius and the signless Laplacian spectral radius of G, denoted by �(G) and q(G), respectively. When G is connected, A(G) and Q(G) are nonegative irreducible matrix. By the Perron-Frobenius theory, �(G) is simple and has a unique positive unit eigenvector, so does q(G). We refer to such the eigenvector corresponding to q(G) as the Perron vector of G. Two distinct edges in a graph G are independent if they are not adjacent in G. A set of pairwise independent edges of G is called a matching in G. A matching of
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固定匹配数单环图的无符号拉普拉斯谱半径
在所有匹配数固定的单环图中,确定无符号拉普拉斯谱半径最大的图。分别。A(G)和Q(G)的最大特征值分别称为G的谱半径和无符号拉普拉斯谱半径,分别用�(G)和Q(G)表示。当G连通时,A(G)和Q(G)为非负不可约矩阵。根据Perron-Frobenius理论,(G)是简单的,并且具有唯一的正单位特征向量,q(G)也是如此。我们把与q(G)相对应的特征向量称为G的Perron向量。如果图G中的两条不同的边在G中不相邻,则它们是独立的。G的一对独立边的集合称为G中的匹配
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