The spectral radius of tricyclic graphs with n vertices and k pendent vertices

Some results on the spectral radius of generalized ∞ and θ-digraphs

“…We know, by Geng and Li [6], that a tricyclic graph G contains at least three cycles and at most seven cycles, furthermore, there do not exist five cycles in G. Then it is easy to see that the strongly connected digraph G which contains exactly three directed cycles, must belong to one of the above fifteen types (as shown in Fig. 4).…”

Tricyclic graphs with exactly two main eigenvalues

“…It follows from [3] that there are eight types of bases for tricyclic graphs, say, T , = 1 8, which are depicted in Figure 1. …”

The (signless) Laplacian spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices

“…For terminology and notation not defined here, we refer the readers to [1], [2], [4]- [6], [10], [12], [13], [17], [18] and the references therein.…”

“…Several graph spectra, i.e., spectra of A(G), L(G) and Q(G), have been defined in [3]. The spectra of A(G), L(G) are well studied (for instance see [4], [6], [8], [12], [13]), but the spectrum of Q(G) seems to be less well known. It is not until recent years, some researchers found that the spectrum of Q(G) has a strong connection with the structure of the graph (see [7], [10]).…”

“…In this direction, Wu et al [17] determined the unique tree with the largest spectral radius in the class of trees with n vertices and k pendant vertices, and Guo [9] identified the graphs with the largest spectral radius in the class of unicyclic and bicyclic graphs with n vertices and k pendant vertices, respectively. Very recently, Geng et al [6] obtained the unique tricyclic graph with the largest spectral radius in the class of tricyclic graphs with n vertices and k pendant vertices. In this paper, we shall consider the similar problem for signless Laplacian spectral radius and Laplacian spectral radius.…”