Factorizations of complete graphs into trees with at most four non-leave vertices

We give a complete characterization of trees with at most four non-leave vertices, which factorize the complete graph K 2n

On distance magic labeling of graphs

Distance magic labeling of a graph of order n is a bijection f : V → {1, 2, ... , n} with the property that there is a positive integer constant k such that for any vertex x, ΣyϵN(x)f(y) = k, where N(x) is the set of vertices adjacent to x. In this paper, we prove new results about the distance magicness of graphs that have minimum degree one or two. Moreover, we construct distance magic labeling for an infinite family of non-regular graphs

Some remarks on domination

We prove a conjecture of Favaron et al. that every graph of order n and minimum degree at least three has a total dominating set of size at least n/2. We also present several related results about: (1) extentions to graphs of minimum degree two, (2) examining graphs where the bound is tight, and (3) a type of bipartite domination and its relation to transversals in hypergraphs

Decompositions of complete bipartite and tripartite graphs into selfcomplementary factors with finite diameters

We completely determine the spectrum of the complete bipartite and tripartite graphs that are decomposable into two isomorphic factors with a finite diameter