Add to ORKGAmong all trivalent graphs on n vertices, let Gn be one with the smallest possible eigenvalue gap. (The eigenvalue gap is the difference between the two largest eigenvalues of the adjacency matrix; for regular graphs, it equals the second smallest eigenvalue of the Laplacian matrix.) We show that Gn is unique for each n and has maximum diameter. This extends work of Guidu-li and solves a conjecture implicit in a paper of Bussemaker, ^obelji}, Cvetkovi} and Seidel. Depending on n, the graph Gn may not be the only one with maximum diameter. We thus also determine all cubic graphs with maximum diameter for a given number n of vertices. Keywords trivalent graphs eigenvalue ga
AbstractWe improve some recent results on graph eigenvalues. In particular, we prove that if G is a ...
AbstractLet G be a simple graph. Let λ1(G) and μ1(G) denote the largest eigenvalue of the adjacency ...
AbstractLet λ1(G)⩾⋯⩾λn(G) be the eigenvalues of a graph G. We explore the distribution of eigenvalue...
Among all trivalent graphs on n vertices, let Gn be one with the smallest possible eigenvalue gap. (...
AbstractIn this paper we consider graphs with three distinct eigenvalues and, we characterize those ...
AbstractSuppose a graph G have n vertices, m edges, and t triangles. Letting λn(G) be the largest ei...
An upper bound is given on the minimum distance between i subsets of same size of a regular graph in...
AbstractLet G be a simple graph of order n with t triangle(s). Also let λ1(G),λ2(G),…,λn(G) be the e...
AbstractLet G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian o...
If μm and dm denote, respectively, the m-th largest Laplacian eigenvalue and the m-th largest vertex...
AbstractWe show that every limit point of the kth largest eigenvalues of graphs is a limit point of ...
AbstractA tricyclic graph of order n is a connected graph with n vertices and n+2 edges. In this pap...
Suppose a graph G have n vertices, m edges, and t triangles. Letting λn(G) be the largest eigenvalue...
Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] ...
We classify the connected graphs with precisely three distinct eigenvalues and second largest eigenv...
AbstractWe improve some recent results on graph eigenvalues. In particular, we prove that if G is a ...
AbstractLet G be a simple graph. Let λ1(G) and μ1(G) denote the largest eigenvalue of the adjacency ...
AbstractLet λ1(G)⩾⋯⩾λn(G) be the eigenvalues of a graph G. We explore the distribution of eigenvalue...
Among all trivalent graphs on n vertices, let Gn be one with the smallest possible eigenvalue gap. (...
AbstractIn this paper we consider graphs with three distinct eigenvalues and, we characterize those ...
AbstractSuppose a graph G have n vertices, m edges, and t triangles. Letting λn(G) be the largest ei...
An upper bound is given on the minimum distance between i subsets of same size of a regular graph in...
AbstractLet G be a simple graph of order n with t triangle(s). Also let λ1(G),λ2(G),…,λn(G) be the e...
AbstractLet G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian o...
If μm and dm denote, respectively, the m-th largest Laplacian eigenvalue and the m-th largest vertex...
AbstractWe show that every limit point of the kth largest eigenvalues of graphs is a limit point of ...
AbstractA tricyclic graph of order n is a connected graph with n vertices and n+2 edges. In this pap...
Suppose a graph G have n vertices, m edges, and t triangles. Letting λn(G) be the largest eigenvalue...
Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] ...
We classify the connected graphs with precisely three distinct eigenvalues and second largest eigenv...
AbstractWe improve some recent results on graph eigenvalues. In particular, we prove that if G is a ...
AbstractLet G be a simple graph. Let λ1(G) and μ1(G) denote the largest eigenvalue of the adjacency ...
AbstractLet λ1(G)⩾⋯⩾λn(G) be the eigenvalues of a graph G. We explore the distribution of eigenvalue...