New bounds for codes identifying vertices in graphs.
New bounds for the broadcast domination number of a graph
A dominating broadcast on a graph G = (V, E) is a function f: V → {0, 1, ..., diam G} such that f(v) ≤ e(v) (the eccentricity of v) for all v ∈ V and such that each vertex is within distance f(v) from a vertex v with f(v) > 0. The cost of a broadcast f is σ(f) = Σv∈V f(v), and the broadcast number λ b (G) is the minimum cost of a dominating broadcast. A set X ⊆ V(G) is said to be irredundant if each x ∈ X dominates a vertex y that is not dominated by any other vertex in X; possibly y = x. The...
New bounds for union-free families of sets.
New bounds on the number of representation of as a binomial coefficient.
New Bounds on the Signed Total Domination Number of Graphs
In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ(G) ≥ 3 from above by [...] . Also, we prove that γst(T) ≤ n − 2(s − s′) for any tree T of order n, with s support vertices and s′ support vertices...
New characterization of by its noncommuting graph.
New classes of critical kernel-imperfect digraphs
A kernel of a digraph D is a subset N ⊆ V(D) which is both independent and absorbing. When every induced subdigraph of D has a kernel, the digraph D is said to be kernel-perfect. We say that D is a critical kernel-imperfect digraph if D does not have a kernel but every proper induced subdigraph of D does have at least one. Although many classes of critical kernel-imperfect-digraphs have been constructed, all of them are digraphs such that the block-cutpoint tree of its asymmetrical part is a path....
New complexity results for time-constrained dynamical optimal path problems.
New directions in enumerative chess problems.
New edge neighborhood graphs
Let be an undirected simple connected graph, and be an edge of . Let be the subgraph of induced by the set of all vertices of which are not incident to but are adjacent to or . Let be the class of all graphs such that, for some graph , for every edge of . Zelinka [3] studied edge neighborhood graphs and obtained some special graphs in . Balasubramanian and Alsardary [1] obtained some other graphs in . In this paper we given some new graphs in .
New Euler-Mahonian permutation statistics.
New graphs of finite mutation type.
New infinite families of 3-designs from algebraic curves of higher genus over finite fields.
New infinite families of almost-planar crossing-critical graphs.
New infinite families of Ramanujan-type congruences modulo 9 for overpartition pairs
Let denote the number of overpartition pairs of n. Bringmann and Lovejoy (2008) proved that for n ≥ 0, . They also proved that there are infinitely many Ramanujan-type congruences modulo every power of odd primes for . Recently, Chen and Lin (2012) established some Ramanujan-type identities and explicit congruences for . Furthermore, they also constructed infinite families of congruences for modulo 3 and 5, and two congruence relations modulo 9. In this paper, we prove several new infinite...
New lower bound for multicolor Ramsey numbers for even cycles.
New lower bound formulas for multicolored Ramsey numbers.
New lower bound on the number of ternary square-free words.
New lower bounds for orthogonal drawings.
New lower bounds for some multicolored Ramsey numbers.