A connected graph G=(V,E) with m edges is called universal antimagic if for each set B of m positive integers there is an bijective function f:E→B such that the function f˜:V→N defined at each vertex v as the sum of all ...

Hartsfield and Ringel in 1990 conjectured that any connected graph with q >= 2 edges has an edge labeling f with labels in the set {1,..., q}, such that for every two distinct vertices u and v, f(u) not equal= f(v), where ...

We consider two variations of graph total domination, namely, k-tuple total domination and total {k}-domination (for a fixed positive integer k). Their related decision problems are both NP-complete even for bipartite ...

A biclique of a graph G is a maximal induced complete bipar tite subgraph of G. Given a graph G, the biclique matrix of G is a {0,1, -1} matrix having one row for each biclique and one column for each vertex of G, and such ...

A b-coloring of a graph is a proper coloring such that every color class contains a vertex that is adjacent to all other color classes. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number t such ...

A graph G = (V, E) is weighted-k-antimagic if for each w : V -> R, there is an injective function f : E -> {1,...,vertical bar E vertical bar + k} such that the following sums are all distinct: for each vertex u, Sigma(v:uv ...

Given a positive integer k, the {k}-packing function problem ({k}PF) is to find in a given graph G, a function f of maximum weight that assigns a non-negative integer to the vertices of G in such a way that the sum of f(v) ...

We show that for any 2-local colouring of the edges of the balanced complete bipartite graph Kn,n, its vertices can be covered with at most 3 disjoint monochromatic paths. And, we can cover almost all vertices of any ...

We show that for any coloring of the edges of the complete bipartite graph Kn,n with three colors there are five disjoint monochromatic cycles which together cover all but o(n) of the vertices. In the same situation, 18 ...