In this paper, some new properties are presented to the extremal graphs with largest (signless Laplacian) spectral radii in the set of all the connected graphs with prescribed degree sequences, via which we determine all the extremal tricyclic graphs in the class of connected tricyclic graphs with prescribed degree sequences, and we also prove some majorization theorems of tricyclic graphs with...

Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n + 2$ edges, and tetracyclic if $G$ has exactly $n + 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n...

The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we investigate Laplacian spread of graphs, and prove that there exist exactly five types of tricyclic graphs with maximum Laplacian spread among all tricyclic graphs of fixed order.

Topological indices are a class of numerical invariants that predict certain physical and chemical properties molecules. Recently, two novel topological indices, named as Sombor index reduced index, were introduced by Gutman, defined where denotes the degree vertex in . In this paper, our aim is to order trees, unicyclic graphs, bicyclic graphs tricyclic with respect index. We determine first f...