4 citations · 7 across the 11 of their papers we have counts for
14 papers
Forbidden stars in multidimensional - matrices and visibility of lattice points
Zoltán Füredi, Balázs Keszegh, Paul Manuel
A -dimensional - matrix of size can be considered as a Boolean function $M: B(n_1\times n_2\times \dots \times n_d) \to \{ 0,1\}…
Properties of Villarceau Torus
Paul Manuel
Villarceau torus is a discrete graph theory model of spiral torus which is called Helical Toroidal Electron Model in Physics. It also represents the double stranded helix model of…
General Position Problem of Butterfly Networks
R. Prabha, S. Renukaa Devi, Paul Manuel
A general position set S is a set S of vertices in G(V,E) such that no three vertices of S lie on a shortest path in G. Such a set of maximum size in G is called a gpset of G and i…
Geodesic packing in graphs
Paul Manuel, Bostjan Bresar, Sandi Klavzar
Given a graph , a geodesic packing in is a set of vertex-disjoint maximal geodesics, and the geodesic packing number of , ${\gpack}(G)$, is the maximum cardinality of a g…
The geodesic cover problem for butterfly networks
Paul Manuel, Sandi Klavzar, R. Prabha +1
A geodesic cover, also known as an isometric path cover, of a graph is a set of geodesics which cover the vertex set of the graph. An edge geodesic cover of a graph is a set of geo…
Generalization of edge general position problem
Paul Manuel, R. Prabha, Sandi Klavzar
The edge geodesic cover problem of a graph is to find a smallest number of geodesics that cover the edge set of . The edge -general position problem is introduced as the…
The geodesic transversal problem on some networks
Paul Manuel, Bostjan Bresar, Sandi Klavzar
A set S of vertices of a graph G is a geodesic transversal of G if every maximal geodesic of G contains at least one vertex of S. We determine a smallest geodesic transversal in ce…
The geodesic-transversal problem
Paul Manuel, Boštjan Brešar, Sandi Klavžar
A maximal geodesic in a graph is a geodesic (alias shortest path) which is not a subpath of a longer geodesic. The geodesic-transversal problem in a graph is introduced as the…
On the isometric path partition problem
Paul Manuel
The isometric path cover (partition) problem of a graph is to find a minimum set of isometric paths which cover (partition) the vertex set of the graph. The isometric path cover (p…
Revisiting path-type covering and partitioning problems
Paul Manuel
Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination proble…
The graph theory general position problem on some interconnection networks
Paul Manuel, Sandi Klavžar
Given a graph , the (graph theory) general position problem is to find the maximum number of vertices such that no three vertices lie on a common geodesic. This graph invariant…
Graph theory general position problem
Paul Manuel, Sandi Klavžar
The classical no-three-in-line problem is to find the maximum number of points that can be placed in the grid so that no three points lie on a line. Given a set of…
Strong geodetic problem in grid like architectures
Sandi Klavžar, Paul Manuel
A recent variation of the classical geodetic problem, the strong geodetic problem, is defined as follows. If is a graph, then is the cardinality of a smallest ver…
Strong geodetic problem in networks: computational complexity and solution for Apollonian networks
Paul Manuel, Sandi Klavžar, Antony Xavier +2
The geodetic problem was introduced by Harary et al. In order to model some social network problems, a similar problem is introduced in this paper and named the strong geodetic pro…