Sylwia Cichacz

Arbitrarily vertex decomposable caterpillars with four or five leaves

A graph G of order n is called arbitrarily vertex decomposable if for each sequence (a1, . . . , ak) of positive integers such that a1+. . .+ak = n there exists a partition (V1, . . . , Vk) of the vertex set of G such that for each i ∈ {1, . . . , k}, Vi induces a connected subgraph of G on ai vertices. D. Barth and H. Fournier showed that if a tree T is arbitrarily vertex decomposable, then T has maximum degree at most 4. In this paper we give a complete characterization of arbitrarily vertex decomposable caterpillars with four leaves. We also describe two families of 292 S. Cichacz, A. Görlich, A. Marczyk, J. PrzybyÃlo and ... arbitrarily vertex decomposable trees with maximum degree three or four.

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 ) .

Group irregularity strength of connected graphs

We investigate the group irregularity strength (

Note on group distance magic complete bipartite graphs

s_g(G)

Group sum chromatic number of graphs

sg(G)) of graphs, that is, we find the minimum value of

Distance magic graphs G × C n

s