Add to ORKGWe prove a number of relations between the number of cliques of a graph G and the largest eigenvalue (G) of its adjacency matrix. In particular, writing ks (G) for the number of s-cliques of G, we show that, for all r 2; r+1 (G) (r + 1) kr+1 (G) + rX s=2 (s 1) ks (G)r+1s (G); and, if G is of order n; then kr+1 (G
We prove three results about the spectral radius (G) of a graph G: (a) Let Tr (n) be the r-partite ...
This paper is a survey on the upper and lower bounds for the largest eigenvalue of the Laplacian mat...
The distance Laplacian matrix of a connected graph G is defined as ℒG=TrG−DG, where DG is the distan...
We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue...
AbstractWe prove a number of relations between the number of cliques of a graph G and the largest ei...
AbstractThe eigenvalues of a graph are the eigenvalues of its adjacency matrix. This paper presents ...
Let G be a simple connected graph with n vertices, m edges and degree sequence: d1 ≥ d2 · · · ≥ d...
AbstractLet G be a simple connected graph with n vertices, m edges and degree sequence: d1⩾d2⩾⋯⩾dn. ...
AbstractWe obtain a sequence k1(G) ≤ k2(G) ≤ … ≤ kn(G) of lower bounds for the clique number (size o...
This paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of g...
AbstractLet G be a simple connected graph with n vertices and m edges. Let δ(G)=δ be the minimum deg...
AbstractGiven a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its...
Given a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique ...
Let λ (G) be the largest eigenvalue of the adjacency matrix of a graph G. We show that if G is Kp+1-...
Let G be a graph of order n and μ (G) be the largest eigenvalue of its adjacency matrix. Let over(G,...
We prove three results about the spectral radius (G) of a graph G: (a) Let Tr (n) be the r-partite ...
This paper is a survey on the upper and lower bounds for the largest eigenvalue of the Laplacian mat...
The distance Laplacian matrix of a connected graph G is defined as ℒG=TrG−DG, where DG is the distan...
We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue...
AbstractWe prove a number of relations between the number of cliques of a graph G and the largest ei...
AbstractThe eigenvalues of a graph are the eigenvalues of its adjacency matrix. This paper presents ...
Let G be a simple connected graph with n vertices, m edges and degree sequence: d1 ≥ d2 · · · ≥ d...
AbstractLet G be a simple connected graph with n vertices, m edges and degree sequence: d1⩾d2⩾⋯⩾dn. ...
AbstractWe obtain a sequence k1(G) ≤ k2(G) ≤ … ≤ kn(G) of lower bounds for the clique number (size o...
This paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of g...
AbstractLet G be a simple connected graph with n vertices and m edges. Let δ(G)=δ be the minimum deg...
AbstractGiven a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its...
Given a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique ...
Let λ (G) be the largest eigenvalue of the adjacency matrix of a graph G. We show that if G is Kp+1-...
Let G be a graph of order n and μ (G) be the largest eigenvalue of its adjacency matrix. Let over(G,...
We prove three results about the spectral radius (G) of a graph G: (a) Let Tr (n) be the r-partite ...
This paper is a survey on the upper and lower bounds for the largest eigenvalue of the Laplacian mat...
The distance Laplacian matrix of a connected graph G is defined as ℒG=TrG−DG, where DG is the distan...