On the Distance Signless Laplacian Spectral Radius of Bicyclic Graphs
Received:March 25, 2022  Revised:June 26, 2022
Key Words: distance signless Laplacian matrix   spectral radius   bicyclic graph  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11971054).
Author NameAffiliation
Yubin GAO Department of Mathematics, North University of China, Shanxi 030051, P. R. China 
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      The distance signless Laplacian matrix of a connected graph $G$ is defined as $\mathcal{Q}(G)=Tr(G)+D(G)$, where $Tr(G)$ is the diagonal matrix of the vertex transmissions in $G$ and $D(G)$ is the distance matrix of $G$. The largest eigenvalue of the distance signless Laplacian matrix is called the distance signless Laplacian spectral radius of $G$. In this paper, we determine the unique graph with the maximum distance signless Laplacian spectral radius among all the bicyclic graphs with given order.
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