On The Spectral Radius Of Some Tricyclic Graphs With N Vertices And Girth G

For a tricyclic graph T, the base of T is the minimal tricyclic subgraph of T. There are seven types of bases for tricyclic graphs, say,(?)i,i=1,2,…,7. Let (?)i(n,g) be the set of all tricyclic graphs on n vertices with girth g having the base of type (?)i, i= 1,2,…,7. In this paper, we determine the unique graph with the largest spectral radius among all the graphs in (?)i(n,g) for i=1,2,3,4. We also determine the unique graph with the largest spectral radius among all the graphs in (?)i(n,g). Moreover, the largest spectral radii are decreasing functions on g.