AbstractWe prove a number of relations between the number of cliques of a graph G and the largest eigenvalue μ(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,μr+1(G)⩽(r+1)kr+1(G)+∑s=2r(s−1)ks(G)μr+1−s(G), and, if G is of order n, thenkr+1(G)⩾(μ(G)n−1+1r)r(r−1)r+1(nr)r+1
AbstractWe prove three results about the spectral radius μ(G) of a graph G:(a)Let Tr(n) be the r-par...
Abstract. Let G =(V,E) be a simple connected graph with n vertices and e edges. Assume that the vert...
Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any ...
We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue...
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 and m edges. Let δ(G)=δ be the minimum deg...
AbstractLet G be a simple connected graph with n vertices, m edges and degree sequence: d1⩾d2⩾⋯⩾dn. ...
Let λ (G) be the largest eigenvalue of the adjacency matrix of a graph G. We show that if G is Kp+1-...
AbstractWe obtain a sequence k1(G) ≤ k2(G) ≤ … ≤ kn(G) of lower bounds for the clique number (size o...
Given a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique ...
AbstractThe eigenvalues of a graph are the eigenvalues of its adjacency matrix. This paper presents ...
AbstractGiven a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its...
Let G be a graph of order n and μ (G) be the largest eigenvalue of its adjacency matrix. Let over(G,...
This paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of g...
Let μ (G) and μmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G....
AbstractWe prove three results about the spectral radius μ(G) of a graph G:(a)Let Tr(n) be the r-par...
Abstract. Let G =(V,E) be a simple connected graph with n vertices and e edges. Assume that the vert...
Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any ...
We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue...
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 and m edges. Let δ(G)=δ be the minimum deg...
AbstractLet G be a simple connected graph with n vertices, m edges and degree sequence: d1⩾d2⩾⋯⩾dn. ...
Let λ (G) be the largest eigenvalue of the adjacency matrix of a graph G. We show that if G is Kp+1-...
AbstractWe obtain a sequence k1(G) ≤ k2(G) ≤ … ≤ kn(G) of lower bounds for the clique number (size o...
Given a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique ...
AbstractThe eigenvalues of a graph are the eigenvalues of its adjacency matrix. This paper presents ...
AbstractGiven a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its...
Let G be a graph of order n and μ (G) be the largest eigenvalue of its adjacency matrix. Let over(G,...
This paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of g...
Let μ (G) and μmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G....
AbstractWe prove three results about the spectral radius μ(G) of a graph G:(a)Let Tr(n) be the r-par...
Abstract. Let G =(V,E) be a simple connected graph with n vertices and e edges. Assume that the vert...
Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any ...
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