Let G = ( V , E ) be a simple undirected graph. A labeling f : )→{1, …, k } is local inclusive d -distance vertex irregular of if every adjacent vertices x y ∈ have distinct weights, with the weight w ), sum labels whose distance from at most . The irregularity strength lidis least number for which there exists In this paper, we prove conjecture on 1 tree and generalize result block graph using...

The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (D) = V (C1) ∪ V (C2), and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (C1) ∪ V (C2...

In the context of two-path convexity, we study the rank, Helly number, Radon number, Caratheodory number, and hull number for multipartite tournaments. We show the maximum Caratheodory number of a multipartite tournament is 3. We then derive tight upper bounds for rank in both general multipartite tournaments and clone-free multipartite tournaments. We show that these same tight upper bounds ho...

Let the star on n vertices, namely K 1, − 1 be denoted by S . If every two coloring of edges a complete balanced multipartite graph j × s there is copy in first color or m second color, then we will say → ( , ) The size Ramsey number smallest natural such that In this paper, obtain exact values numbers for ≥ 3 and

We propose a scheme for generating multipartite entangled coherent states via entanglement swapping, with an example of a physical realization in ion traps. Bipartite entanglement of these multipartite states is quantified by the concurrence. We also compute multipartite entanglement for certain systems. Finally we establish that these results for entanglement can be applied to more general mul...

A tournament is an orientation of a complete graph, and in general a multipartite or c-partite tournament is an orientation of a complete c-partite graph. If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is de6ned by ig(D) = max{d+(x); d−(x)} − min{d+(y); d−(y)} over all vertices x and y o...

In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

The interval number of a graph G, denoted i(G), is the least positive integer t for which G is the intersection graph of a family of sets each of which is the union of at most t cIosed intervals of the real line IR. Trotter and Harary showed that the interval number of the complete bipartite graph K(m, n) is [(mn + I)/(m + n)]. Matthews showed that the interval number of the complete multiparti...