On the singular graph and the Weyr characteristic of an M-matrix.
On the size of a maximal induced tree in a random graph
On the size of dissociated bases.
On the size of minimal unsatisfiable formulas.
On the smallest minimal blocking sets in projective space generating the whole space.
On the spectra of Johnson graphs.
On the spectral radii of quasi-tree graphs and quasi-unicyclic graphs with k pendent vertices.
On the spectral radius of bicyclic graphs
On the Spectral Radius of Connected Graphs
On the spectral radius of -shape trees
Let be the adjacency matrix of . The characteristic polynomial of the adjacency matrix is called the characteristic polynomial of the graph and is denoted by or simply . The spectrum of consists of the roots (together with their multiplicities) of the equation . The largest root is referred to as the spectral radius of . A -shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by
On the spectrum of resolvable orthogonal arrays invariant under the Klein group K4.
On the spectrum of the derangement graph.
On the sprectra of certain classes of Room frames.
On the stability for pancyclicity
A property P defined on all graphs of order n is said to be k-stable if for any graph of order n that does not satisfy P, the fact that uv is not an edge of G and that G + uv satisfies P implies . Every property is (2n-3)-stable and every k-stable property is (k+1)-stable. We denote by s(P) the smallest integer k such that P is k-stable and call it the stability of P. This number usually depends on n and is at most 2n-3. A graph of order n is said to be pancyclic if it contains cycles of all lengths...
On the Stanley-Wilf conjecture for the number of permutations avoiding a given pattern.
On the Steiner 2-edge connected subgraph polytope
In this paper, we study the Steiner 2-edge connected subgraph polytope. We introduce a large class of valid inequalities for this polytope called the generalized Steiner F-partition inequalities, that generalizes the so-called Steiner F-partition inequalities. We show that these inequalities together with the trivial and the Steiner cut inequalities completely describe the polytope on a class of graphs that generalizes the wheels. We also describe necessary conditions for these inequalities to...
On the strong Arnol'd hypothesis and the connectivity of graphs.
On the strong metric dimension of the strong products of graphs
Let G be a connected graph. A vertex w ∈ V.G/ strongly resolves two vertices u,v ∈ V.G/ if there exists some shortest u-w path containing v or some shortest v-w path containing u. A set S of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G. It is well known that the problem of computing this invariant is NP-hard. In this paper we study...
On the strong parity chromatic number
A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of plane graphs.
On the structural result on normal plane maps
We prove the structural result on normal plane maps, which applies to the vertex distance colouring of plane maps. The vertex distance-t chromatic number of a plane graph G with maximum degree Δ(G) ≤ D, D ≥ 12 is proved to be upper bounded by . This improves a recent bound , D ≥ 8 by Jendrol’ and Skupień, and the upper bound for distance-2 chromatic number.