Search

A graph G(p, q) is said to have an edge-magic total labeling if there exists a bijective function f: V(G) ∪ E(G) → {1, 2, ...,p + q}, such that for any edge uv∊E(G) the condition f(u)+f(v)+f(uv)=k is satisfied, k is a constant. In this paper, a new algorithm, based on the graph generate algorithm, is designed to obtain the edge-magic total labeling of the unicyclic graphs. Some theorems about unicyclic graphs are also deduced from the algorithm's results. It's believed that the algorithm proposed is innovative and can be adopted by other researchers. [ABSTRACT FROM AUTHOR]

A graph G(p,q) is said to have an edge-magic total labeling if there exists a bijective function f: V (G) ∪ E(G) → {1,2, · · ·, p+q}, such that for any edge uv of G, f(u)+f(v)+ f(uv) = k, k is a constant. Moreover, G is said to have a super edge-magic total labeling if f(V (G)) = {1, 2, · · ·, p}. We propose a new algorithm, based on the graph generation method, to solve the problem of super edge-magic total labeling of graphs with a large number of vertices. First, we introduce a new operation called generalized coalescence, then we generate the adjacent matrices of graphs composed of fans, circle and star. Second, we input these matrices to our proposed algorithm. Third, if a graph exist a super edge-magic total labeling, the algorithm will output the corresponding super edge-magic total labeling matrices. Otherwise, no super edge-magic total labeling exists for the graphs involved. Fourth, from the results, we conclude that regular labels are found in some of the graphs involved. Our algorithm can distinguish super edge-magic total labeling graphs from those graphs which don’t have. [ABSTRACT FROM AUTHOR]