Showing papers in "Discrete Mathematics in 2012"

TL;DR: A survey of work on perfect state transfer and related questions can be found in this article, where the emphasis is almost entirely on the mathematics, and some new results and open questions are discussed.

TL;DR: This work establishes global structure by bounding the number of colors that can induce a spanning and connected subgraph within colorings free of these subgraphs, and shows that the bounds are sharp.

TL;DR: The r -Whitney–Lah numbers and the r -Dowling polynomials associated with the Dowling lattice are developed and their combinatorial interpretations are given.

TL;DR: The metric dimension of the lexicographic product of graphs $G$ and $H$ is studied in terms of the order of G and the adjacency metric Dimension of H is obtained.

TL;DR: It is shown that if the chromatic number of the zero-divisor graph is finite, then the Chromatic numberOf the annihilating-ideal graph of a commutative ring is finite too, and it is proved that A G ( R ) is bipartite if and only if A G(R) is triangle-free.

TL;DR: It is proved that if G=(V,E) is an undirected graph then the size of a contagious set is bounded by @?"v"@?"Vmin{1,kd(v)+1} (where d(v) is the degree of v).

TL;DR: All inv - and maj -Wilf equivalences for any Π ⊆ S 3 .

TL;DR: For each k>=2, the authors construct a k-connected graph which does not contain two completely independent spanning trees, which disproves a conjecture of Hasunuma.

TL;DR: Properties of the generating functions for the number of interior and left peaks over the symmetric group, including recurrence relations, generating functions and real-rootedness, are studied.

TL;DR: The question whether Q d ( f ) is an isometric subgraph of Q d is studied and the question is completely solved for strings f of length at most five and for strings consisting of at most three blocks.

TL;DR: This paper provides a complete description of the complexity status of the problem in subclasses of triangle-free graphs obtained by forbidding a forest with at most 6 vertices and proves polynomial-time solvability of theproblem in many classes of this type.

TL;DR: It is shown that the locating-total domination number of a claw-free cubic graph is at most one-half its order and the graphs achieving this bound are characterized.

TL;DR: The fractional metric dimension of G is defined as dim"f(G)=min{|g|:g is a minimal resolving function of G}, where |g|=@?"v"@?"Vg(v), and this parameter is studied.

TL;DR: This paper confirms a conjecture of Fujita, Kaneko, Schiermeyer, and Suzuki that states AR(M"k,2k)=max{2k-32+3,k-22+k^2-2}, where M"k is a matching of size k>=3.

TL;DR: The smallest size of any dynamic monopoly of G, with a given threshold assignment, is denoted by dyn(G), and the concept of a resistant subgraph is defined and its relationship with dynamic monopolies is shown.

TL;DR: In this paper, the authors highlight local food consumption which was favored by 83% of French people in 2010, and the consumer perspective and positioning strategies on this market are developed around four motivations: reduction of health risks, rediscovery of taste, the desire for sustainable consumption and the search for social relationships.

TL;DR: Two characterizations of the graphs on which k cops have a winning strategy in the game of Cops and Robber are given in terms of an order relation and a vertex ordering.

TL;DR: It is shown that if G is a connected graph of order n ≥ 3 with no isolated vertex, then fd ( G ) ≤ n − 2, and an infinite family of connected graphs achieving equality in this bound is constructed.

TL;DR: A sharp upper bound is established on the Roman domination numbers of graphs with minimum degree at least 3 and on the connected, big-claw-free and big-net-free graphs.

TL;DR: A combinatorial interpretation in terms of weighted Łukasiewicz paths is provided and several large classes of examples are looked at, showing how Riordan arrays tend to be related to each other.

TL;DR: The structure of G v, the group G of its automorphisms, is determined when X has valency 5 and G v is non-solvable.

TL;DR: This article considers the first-order properties and the probabilities p=N^-^@a for rational @a for Erdos-Renyi random graphs G(N,p), finding the zero-one law in ordinary sense for these graphs doesn't hold.

TL;DR: Three new families of digraphs are introduced, two of them generalizing transitive and quasi-transitiveDigraphs respectively, and it is proved that a k -transitive digraph has an n -kernel for every n ?

TL;DR: In this paper, Diestel et al. present a survey of the topological approach to the study of locally finite graphs with ends, where topological arcs and circles are assumed to play the role played in finite graphs by paths and cycles.

TL;DR: An improvement on Babai's most general bound for the metric dimension of distance-regular graphs, in the case of H"q(n,d) with n>=d>=4.

TL;DR: New upper bounds are proved on the Thue chromatic number of an arbitrary graph and on the facial Thuechrome number of a plane graph in terms of its maximum degree.

TL;DR: This paper analyzes the cop and robber game with the metric dimension problem for several classes of graphs, including cycles and trees, and concludes that the cop’s goal is to minimize the number of probes required to locate the robber.

TL;DR: The concept of strongly balanced G-design is introduced and strongly balanced path-designs are studied and the spectrum of those path- designs which are balanced, but not strongly balanced is determined.

TL;DR: Using elementary methods, several new Ramanujan type identities and congruences for certain pairs of partition functions are established.

TL;DR: A best possible lower bound on the matching number of connected cubic graphs in terms of their order and odd girth is proved, and all extremal graphs are characterized.