Sequences of Well-Distributed Vertices on Graphs and Spectral Bounds on Optimal Transport

On the Spectral Radius of Graphs with Cut Vertices

The graphs in this paper are simple. The spectral radius, \(G), of a graph G is the largest eigenvalue of its adjacency matrix A(G). For results on the spectral radii of graphs, the reader is referred to [3, 4, 6] and the references therein. When G is connected, A(G) is irreducible and by the Perron Frobenius Theorem, e.g., [1], the spectral radius is simple and has a unique (up to a multiplica...

Sharp Bounds on the PI Spectral Radius

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

A Note on Well Distributed Sequences

New bounds on proximity and remoteness in graphs

The average distance of a vertex $v$ of a connected graph $G$is the arithmetic mean of the distances from $v$ to allother vertices of $G$. The proximity $pi(G)$ and the remoteness $rho(G)$of $G$ are defined as the minimum and maximum averagedistance of the vertices of $G$. In this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...

On the spectral radii of quasi-tree graphs and quasi-unicyclic graphs with k pendent vertices

A connected graph G = (V, E) is called a quasi-tree graph if there exists a vertex u0 ∈ V (G) such that G−u0 is a tree. A connected graph G = (V, E) is called a quasi-unicyclic graph if there exists a vertex u0 ∈ V (G) such that G− u0 is a unicyclic graph. Set T (n, k) := {G : G is a n-vertex quasi-tree graph with k pendant vertices}, and T (n, d0, k) := {G : G ∈ T (n, k) and there is a vertex ...