The Spectral Radius of Bicyclic and Tricyclic Graphs with no Pendant
The sum of the diagonal degree matrix and the adjacency matrix of the graph is called the signless Laplacian matrix,and the signless Laplacian matrix of the connected graph is a non-negative irreducible matrix,and its largest eigenvalue is called the signless Laplacian spectral radius.A graph that satisfies a difference of 1 between the number of edges and vertices is called a Bicyclic graph,and a graph that has a difference of 2 from the number of edges and vertices is called a Tricyclic graph.The spectral problem has always been ahot research problem in graph theory.In this paper,we deter-mine the structure of graphs with maximum signless Laplacian spectral radius in the class of Bicyclic graph and Tricyclic graph with no pendant,respectively.
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