If each minimal dominating set in a graph is minimum set, then the called well-dominated. Since seminal paper on well-dominated graphs appeared 1988, structure of from several restricted classes has been studied. In this we give complete characterization nontrivial direct products that are We prove if strong product well-dominated, both its factors When one graph, other factor being also suffic...

By the sorting method of vertices, the equitable chromatic number and the equitable chromatic threshold of the Cartesian products of wheels with bipartite graphs are obtained. Key–Words: Cartesian product, Equitable coloring, Equitable chromatic number, Equitable chromatic threshold

24 A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection 25 l : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum 26 of the labels on the vertices in the open neighborhood of v, is a constant. 27 In this paper, we show that hypercubes with dimension divisible by four 28 are not distance magic. We also provide some positive results by providing ...

Let G = (V,E) be a graph. For a non-empty subset of vertices S ⊆ V , and vertex v ∈ V , let δS(v) = |{u ∈ S : uv ∈ E}| denote the cardinality of the set of neighbors of v in S, and let S = V − S. Consider the following condition: δS(v) ≥ δS(v) + k, (1) which states that a vertex v has at least k more neighbors in S than it has in S. A set S ⊆ V that satisfies Condition (1) for every vertex v ∈ ...

Sandi Klavžar and Zehui Shao Faculty of Mathematics and Physics, University of Ljubljana, Slovenia Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, China School of Info...

We classify all factors of the Cartesian product of any two nonsingular type III , 0 < < 1, or II1, Chacon transformations, as well as the centralizer of nite Cartesian products of such transformations. AMS 1991 subject classi cation: 28D99.

A nowhere-zero k-flow on a graph G is an assignment of a direction and a non-zero integer in absolute value smaller than k to each edge of G in such a way that, for each vertex, the sum of incoming values equals the sum of outgoing values. Nowhere-zero flow problems evolved from flowcolouring duality to a theory which has a central role in graph theory. There are many important flow problems wh...