On supermagic regular graphs

On Supermagic Regular Graphs

A graph is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. Some constructions of supermagic labellings of regular graphs are described. Supermagic regular complete multipartite graphs and supermagic cubes are characterized.

Some constructions of supermagic non-regular graphs

On Magic and Supermagic Line Graphs

A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. We characterize magic line graphs of general graphs and describe some class of supermagic line graphs of bipartite graphs.

On a Construction of Supermagic Graphs

Given two graphs G and H. The composition of G with H is the graph with vertex set V (G) × V (H) in which (u1, v1) is adjacent to (u2, v2) if and only if u1u2 ∈ E(G) or u1 = u2 and v1v2 ∈ E(H). In this paper, we prove that the composition of regular supermagic graph with a null graph is supermagic. With the help of this result we show that the composition of a cycle with a null graph is always ...

H-supermagic labelings of graphs

A simple graph G admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. The graph G is H−magic if there exists a bijection f : V (G) [ E(G) ! {1, 2, 3, · · · , |V (G) [ E(G)|} such that for every subgraph H0 P of G isomorphic to H. G is said to be H − supermagic if f(V (G)) = {1, 2, 3, · · · , |V (G)|}. In thi...