Now showing items 1-9 of 9
On the complexity of the positive semidefinite zero forcing number
The positive semidefinite zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring and is related to a more conventional version of zero forcing. We establish a relation ...
On the relationship between zero forcing number and certain graph coverings
The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced ...
Intersecting generalized permutations
Minimum number of distinct eigenvalues of graphs
(International Linear Algebra Society, 2013-09)
The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to ...
MIKL´ OS-MANICKAM-SINGHI CONJECTURES ON PARTIAL GEOMETRIES
In this paper we give a proof of the Mikl´os-Manickam-Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, ...
An Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective plane
(SIAM Journal on Discrete Mathematics, 2014)
Let G = PGL(2, q) be the projective general linear group acting on the projec- tive line P_q. A subset S of G is intersecting if for any pair of permutations \pi and \sigma in S, there is a projective point p in P_q such ...
An Erdős-Ko-Rado theorem for the derangement graph of \(PGL_3(q)\) acting on the projective plane
(SIAM J. Discrete Math. 28, 2014)
In this paper we prove an Erdős-Ko-Rado-type theorem for intersecting sets of permutations. We show that an intersecting set of maximal size in the projective general linear group \(PGL_3(q)\), in its natural ...
An Erdős-Ko-Rado theorem for finite \(2\)-transitive groups
(European Journal of Combinatorics, 2016)
We prove an analogue of the classical Erdős-Ko-Rado theorem for intersecting sets of permutations in finite \(2\)-transitive groups. Given a finite group \(G\) acting faithfully and \(2\)-transitively on the set ...