Dalibor Froncek

Some remarks on domination: SOME REMARKS ON DOMINATION

Proof: The proof is by induction on |V (G)| + |E(G)|. The smallest graph as described in the lemma is K1,3, for which the statement holds. This gives the start of our induction. Let x = |X| and y = |Y |. If there exists a vertex v in Y of degree at least 4, then delete any edge e incident to v. The subset A of G− e guaranteed by the inductive hypothesis is adjacent in G to every vertex in Y as desired. So we may assume that the vertices in Y are all of

The existence of selfcomplementary circulant graphs

Abstract All values of n for which there exist a selfcomplementary circulant graph of order n are determined.

Cyclic decompositions of complete graphs into spanning trees

We examine decompositions of complete graphs with an even number of vertices, K2n, into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.

Distance magic circulant graphs

Let G = ( V , E ) be a graph of order n . A distance magic labeling of G is a bijection ? : V ? { 1 , 2 , ? , n } for which there exists a positive integer k such that ? x ? N ( v ) ? ( x ) = k for all v ? V , where N ( v ) is the neighborhood of v . In this paper we deal with circulant graphs C n ( 1 , p ) . The circulant graph C n ( 1 , p ) is the graph on the vertex set V = { x 0 , x 1 , ? , x n - 1 } with edges ( x i , x i + p ) for i = 0 , ? , n - 1 where i + p is taken modulo n . We completely characterize distance magic graphs C n ( 1 , p ) for p odd. We also give some sufficient conditions for p even. Moreover, we also consider a group distance magic labeling of C n ( 1 , p ) .

Strong Isometric Dimension, Biclique Coverings, and Sperner's Theorem

The strong isometric dimension of a graph

Round Robin Tournaments with One Bye and No Breaks in Home-Away Patterns Are Unique

G

Decomposition of complete bipartite graphs into generalized prisms

is the least number

Note on Decomposition of Kn,n into (0,j)-prisms

k

Cluttered Orderings for the Complete Graph

such that

On traceability and 2-factors in claw-free graphs

G