AbstractLet G be a simple graph with least eigenvalue λ and let S be a set of vertices in G which induce a subgraph with mean degree k. We use a quadratic programming technique in conjunction with the main angles of G to establish an upper bound of the form |S|⩽inf{(k+t)qG(t):t>-λ} where qG is a rational function determined by the spectra of G and its complement. In the case k=0 we obtain improved bounds for the independence number of various benchmark graphs
AbstractLet G be a graph on vertex set V=v1,v2,…,vn. Let di be the degree of vi, let Ni be the set o...
In this paper we study the conditions under which the stability number of line graphs, generalized l...
Let F be a set of graphs and for a graph G let F(G) and F (G) denote the maximum order of an induce...
Let G be a simple graph with least eigenvalue λ and let S be a set of vertices in G which ind...
AbstractLet G be a simple connected graph with n vertices and m edges. Denote the degree of vertex v...
Many optimization problems on graphs are reduced to the determination of a subset of vertices of max...
AbstractSuppose that G is a connected graph of order n and girth g<n. Let k be the multiplicity of a...
Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving t...
AbstractIn this paper, we present an elementary proof of a theorem of Serre concerning the greatest ...
AbstractFor a simple graph G, the energy E(G) is defined as the sum of the absolute values of all th...
AbstractLet G be a graph with n vertices and m edges and let μ(G)=μ1(G)⩾⋯⩾μn(G) be the eigenvalues o...
AbstractGiven a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its...
AbstractLet G be a connected k-regular graph of order n. We find a best upper bound (in terms of k) ...
summary:Let $G$ be a graph with $n$ vertices, $m$ edges and a vertex degree sequence $(d_1, d_2, ...
AbstractLet k be a positive integer and let G be a graph of order n⩾k. It is proved that the sum of ...
AbstractLet G be a graph on vertex set V=v1,v2,…,vn. Let di be the degree of vi, let Ni be the set o...
In this paper we study the conditions under which the stability number of line graphs, generalized l...
Let F be a set of graphs and for a graph G let F(G) and F (G) denote the maximum order of an induce...
Let G be a simple graph with least eigenvalue λ and let S be a set of vertices in G which ind...
AbstractLet G be a simple connected graph with n vertices and m edges. Denote the degree of vertex v...
Many optimization problems on graphs are reduced to the determination of a subset of vertices of max...
AbstractSuppose that G is a connected graph of order n and girth g<n. Let k be the multiplicity of a...
Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving t...
AbstractIn this paper, we present an elementary proof of a theorem of Serre concerning the greatest ...
AbstractFor a simple graph G, the energy E(G) is defined as the sum of the absolute values of all th...
AbstractLet G be a graph with n vertices and m edges and let μ(G)=μ1(G)⩾⋯⩾μn(G) be the eigenvalues o...
AbstractGiven a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its...
AbstractLet G be a connected k-regular graph of order n. We find a best upper bound (in terms of k) ...
summary:Let $G$ be a graph with $n$ vertices, $m$ edges and a vertex degree sequence $(d_1, d_2, ...
AbstractLet k be a positive integer and let G be a graph of order n⩾k. It is proved that the sum of ...
AbstractLet G be a graph on vertex set V=v1,v2,…,vn. Let di be the degree of vi, let Ni be the set o...
In this paper we study the conditions under which the stability number of line graphs, generalized l...
Let F be a set of graphs and for a graph G let F(G) and F (G) denote the maximum order of an induce...