Showing papers in "Discrete Mathematics in 2013"

TL;DR: A survey of selected recent results on independent domination in graphs is offered and it is shown that not every vertex in S is adjacent to a vertex in S .

TL;DR: In this paper, the authors survey and extend earlier results on the weight distributions of irreducible cyclic codes, present a divisibility theorem and develop bounds on the weights in IRCDs.

TL;DR: The only improper coloring discussed is injective coloring (any two vertices having a common neighbor should have distinct colors).

TL;DR: A more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs.

TL;DR: The structures in terms of polynomial generators of all such constacyclic codes and their duals are established and it is shown that self-dual cyclic codes of length 3 p s exist only when p = 2, and in such case they are listed.

TL;DR: It is proved that both the cube as well as the Birkhoff polytope do not admit extended formulations with fewer inequalities than these polytopes have facets, and it is shown that every extended formulation of a d -dimensional neighborlypolytope with Ω ( d 2 ) vertices has size.

TL;DR: The general bounds of the metric dimension of a lexicographic product of any connected graph G and an arbitrary graph H are given and it is shown that the bounds are sharp.

TL;DR: A survey of results on light graphs in different families of plane graphs and multigraphs is presented, dealing with the family of all graphs embedded in surfaces other than the sphere.

TL;DR: It is proved that the study of the hyperbolicity on graphs can be reduced to the study in the same graph without its loops and multiple edges, and it is shown how thehyperbolicities of a graph changes upon adding or deleting finitely or infinitely many edges.

TL;DR: It is proved that every graph with maximum average degree at most 14 5 is ( 1, 1) -colorable, and it follows that every planar graph with girth at least 7 is (1, 1 ) - colorable.

TL;DR: A modification of the Harary index in which the contributions of vertex pairs are weighted by the sum of their degrees is introduced, finding the extremal graphs and investigating its behavior under several standard graph products.

TL;DR: A survey on some recent results on generalization of Dirac’s theorem on Hamiltonian graph theory.

TL;DR: A lower bound for the game domination number of a tree in terms of the order and maximum degree is proved and shown to be asymptotically tight.

TL;DR: A conjecture is made that explains why antidirected trees are easier to handle and it is shown that every acyclic k -chromatic digraph contains every oriented tree of order k and a number of approaches are suggested for making further progress on Burr’s conjecture.

TL;DR: It is proved that if H c is a balanced bipartite graph of order 2 n with an edge coloring C such that d c ( u ) > 3 n 5 + 1 for every vertex v ∈ V ( H c ) , then there exists a rainbow C 4 in H c.

TL;DR: It is proved that if a circulant graph of large degree has an efficient dominating set, then either its elements are equally spaced, or the graph is the wreath product of a smaller circulants graph with an efficient dominate set and a complete graph.

TL;DR: The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc of a graph G is the mean value of eccentricities of all vertices of G, which gives a proof of one conjecture and disprove two conjectures by counter examples.

TL;DR: In this article, the authors propose a cartographie des medias sociaux, which permet de mettre en evidence l'heterogeneite des MEDIA sociaules, les specificites des plateformes and de mieux envisager les pratiques marketing adaptees aux configurations sociotechniques identifiees.

TL;DR: This work proves new structural properties of cographs which characterize how a largest clique interacts with the rest of the graph and implies a remarkably simple polynomial time algorithm for Cluster Deletion on cographs.

TL;DR: The anti-Ramsey number of a k -matching in a complete s -uniform hypergraph H on n vertices, denoted by ar ( n , s , k ) , is the smallest integer c such that in any coloring of the edges of H with exactly c colors, there is a k-matching whose edges have distinct colors.

TL;DR: It is shown that the abelian complexity function of the ordinary paperfolding word is a 2-regular sequence.

TL;DR: Grammatical interpretations of the generating functions of these numbers, as well as convolution identities involving these generating functions are obtained, and a connection between alternating runs and Andre permutations is established.

TL;DR: In this article, the authors give sharp upper bounds for v a 1 ≡ (K n, n ) and v a k ≡ ( K n, n ), and prove that v a ∞ ≡ ( G ) ≤ 3 for every planar graph G with girth at least 5 and for every outerplanar graph.

TL;DR: It is proved that the bound holds when Δ ( H ) ≤ 2, and for that case the hypergraphs for which equality holds are characterized, and the extremalhypergraphs in this case are characterized.

TL;DR: In this article, a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor gave a recursion for the inversion polynomial of 321-avoiding permutations.

TL;DR: Improved lower and upper bounds for k of the Cartesian and the direct product of paths are derived and it is shown that for 3 those bounds are tight.

TL;DR: The cycle structures of the set of autotopisms of partial Latin squares are characterized and several related properties were studied and the traditional notion ofpartial Latin square completable to a Latin square is generalized.

TL;DR: The G -supermagicness of a disjoint union of c copies of a graph G is investigated and it is proved that certain subgraph -amalgamation of graphs G is G -Supermagic.