A handicap distance antimagic labeling of a graph G = (V,E) with n vertices is a bijection f : V → {1, 2, . . . , n} with the property that f(xi) = i and the sequence of the weights w(x1), w(x2), . . . , w(xn) (where w(xi) = ∑ xj∈N(xi) f(xj)) forms an increasing arithmetic progression with difference one. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagi...

A balanced bipartition of a graph G is a bipartition V1 and V2 of V (G) such that −1 ≤ |V1| − |V2| ≤ 1. Bollobás and Scott conjectured that if G is a graph with m edges and minimum degree at least 2 then G admits a balanced bipartition V1, V2 such that max{e(V1), e(V2)} ≤ m/3, where e(Vi) denotes the number of edges of G with both ends in Vi. In this note, we prove this conjecture for graphs wi...

This paper deals with the problem of coloring a two-dimensional segmentation result in such a way that each segment has a different color with the constraint that adjacent segments have sufficiently distinct colors to be easily distinguishable by a human viewer. Our solution for this problem is based on a balanced coloring of the neighborhood graph built from the area Voronoi diagram. The balan...

A k-circular-distance-two labeling (or k-c-labeling) of a simple graph G is a vertex-labeling, using the labels 0, 1, 2, · · · , k − 1, such that the “circular difference” (mod k) of the labels for adjacent vertices is at least two, and for vertices of distance-two apart is at least one. The σ-number, σ(G), of a graph G is the minimum k of a k-c-labeling of G. For any given positive integers n ...

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed...

Let G = (V, E) be a graph without isolated vertices. A set D ⊆ V is a d-distance paired-dominating set of G if D is a d-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The minimum cardinality of a d-distance paired-dominating set for graph G is the d-distance paired-domination number, denoted by γd p(G). In this paper, we study the ddistance paired-domination n...

By a game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a nonempty set of payo®s for each coalition of players. It is well-known that balancedness is a su±cient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. But any information on the internal organization of the c...