An equitable k-coloring of an undirected graph G = (V,E) is a partition of its vertices into k disjoint independent sets, such that the cardinalities of any two independent sets differ by at most one. As a variant of the graph coloring problem (GCP), the equitable coloring problem (ECP) concerns finding a minimum k for which an equitable k-coloring exists. In this work, we propose a backtrackin...

We study the complexity of # CSP Δ ( Γ ) , which is problem counting satisfying assignments to instances with constraints from and whose variables can appear at most times. Our main result shows that: (i) if every function in affine, then FP for all Δ, (ii) otherwise, a class called I M 2 large equivalent under approximation-preserving reductions independent sets bipartite graphs, (iii) it NP -...

background: the aim of the study was to discuss on the influential factors of the mode of classification of partition management in the emergency triage. method: retrospectively analyzing the effects of emergency triage of 156 cases who adopted the classification partition management mode during oct 2014 to oct 2015 in xuzhou central hospital (xuzhou, jiangsu province, china). they were divided...

Let D be a simple digraph with vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and ∑x∈N−[v] f(x) ≥ k for each v ∈ V (D), where N[v] consists of v and all vertices of D from which arcs go into v, then f is a signed k-dominating function on D. A set {f1, f2, . . . , fd} of distinct signed k-dominating functions on D with the property that ∑d i=1 fi(x...

In this paper we introduced the concepts of global domination number and domatic in product fuzzy graph is denoted by γg(G) dg(G), respectively determine for several classes obtain Nordhaus-Gaddum type results parameter. Further, some bounds dg(G) are investigated. Also relations between γg(G)(dg(G)) other known parameter Product graphs Finally introduce concept full about done.

The three domatic number problem asks whether a given undirected graph can be partitioned into at least three dominating sets, i.e., sets whose closed neighborhood equals the vertex set of the graph. Since this problem is NP-complete, no polynomial-time algorithm is known for it. The naive deterministic algorithm for this problem runs in time 3n, up to polynomial factors. In this paper, we desi...