Ludovít Niepel

Connectivity of iterated line graphs

In this paper we present lower bounds for the connectivity of the i-iterated line graph Li(G) of a graph G. We prove that if G is a connected regular graph and i ≥ 5, then the connectivity of Li(G) is equal to the degree of Li(G), that is, the connect ivity of Li(G) attains its theoretical maximum (we remark that the bound on i is best possible). Moreover, if a hypothesis on the growth of the minimum degree of the i-iterated line graph is true, then an analogous result is true for an arbitrary graph G if i is sufficiently large.

Diameter in iterated path graphs

Abstract If G is a graph, then its path graph, P k (G) , has vertex set identical with the set of paths of length k in G , with two vertices adjacent in P k (G) if and only if the corresponding paths are ‘consecutive’ in G . We study the behavior of diam (P 2 i (G)) as a function of i , where P 2 i (G) is a composition P 2 (P 2 i−1 (G)) , with P 2 0 (G)=G .

Connectivity of path graphs

In the paper we present lower bounds for the connectivity of a path graph P2(G) of a graph G. Let δ ≥ 3 be the minimum degree of G. We prove that if G is a connected graph, then P2(G) is at least (δ−1)connected; and if G is 2-connected, then P2(G) is at least (2δ−2)connected. We remark that if G is a δ-regular graph then P2(G) is (2δ−2)-regular, and hence, if G is 2-connected then P2(G) is (2δ−2)connected; its theoretical maximum.

Hybrid local search approximation algorithm for solving the capacitated Max-K-cut problem

In this article we propose a new hybrid local search approximation algorithm for solving the capacitated Max-k-cut problem and contrast its performance with two local search approximation algorithms. The first of which uses a swapping neighborhood search technique, whereas the second algorithm uses a vertex movement method. We analyze the behavior of the three algorithms with respect to running time complexity, number of iterations performed and the total weight sum of the cut edges. The experimental results show that our proposed hybrid algorithm outperforms its rivals at all levels.

A methodology for discovering spatial co-location patterns

Spatial co-location patterns represent the subsets of events (services/features) whose instances are frequently located together in a geographic space. The co-location patterns discovery presents challenges since the instances of spatial events are embedded in a continuous space and share a variety of spatial relationships. In this paper, we provide a study based on some previous approaches, the concepts that were used, and some of their limitations. We propose a methodology which overcomes the shortcomings of some other approaches. This methodology is based on a spatial access method (KD-tree) with its basic operations and the apriori generation algorithm. The results of conducted experimentation show the correctness and completeness of our approach. The results also illustrate the effect of input data on the performance.

Locating-paired-dominating sets in square grids

A set S of vertices of a graph G is paired-dominating if S induces a matching in G and S dominates all vertices of G . A set S ? V ( G ) is locating if for any two distinct vertices u , v ? V ( G ) ? S , N ( u ) ? S ? N ( v ) ? S , where N ( u ) and N ( v ) are open neighborhoods of vertices u and v . We give a complete characterization of locating-paired-dominating sets with minimal density in the infinite square grid Z 2 .

Histories in path graphs

For a given graph G and a positive integer r the r-path graph, Pr(G), has for vertices the set of all paths of length r in G. Two vertices are adjacent when the intersection of the corresponding paths forms a path of length r − 1, and their union forms either a cycle or a path of length k+1 in G. Let P k r (G) be the k-iteration of r-path graph operator on a connected graph G. Let H be a subgraph of P k r (G). The k-history P r (H) is a subgraph of G that is induced by all edges that take part in the recursive definition of H . We present some general properties of k-histories and give a complete characterization of graphs that are k-histories of vertices of 2-path graph operator.

Radii and centers in iterated line digraphs

We show that the out-radius and the radius grow linearly, or “almost” linearly, in iterated line digraphs. Further, iterated line digraphs with a prescribed out-center, or a center, are constructed. It is shown that not every line digraph is admissible as an out-center of line digraph.