Super Edge Least-Magic Graphs

A (p, q)-graph G = (V, E) is said to be super edge—magic if there exists a bijection f fromV ∪ E to {1, 2, 3,…, p + q } with vertices maps to {1, 2, 3,…, p} such that for all edges uv of G, f(u) + f(v) + f(uv) is a constant and bijection so denned is called a super edge— magic labeling of G, For any super edge—magic labeling of G, there is a constant c(f) such that for all edges uv of G, f(u) + f(v) + f(uv) = c(f) and its range is p + q + 3 ≤ c(f) ≤ 3p. s paper we study super edge—magic graphs with constant c(f) = p+q +3 for at least one f and such graphs are denned as super edge least—magic(SEL—magic) graphs. We investigate the following general results on the structure of SEL—magic graphs including a result, which determines all the regular SEL—magic graphs. SEL—magic graph is either a forest with exactly one nontrivial component, which is a star or has a triangle. an eulerian (p,q)-graph G = (V, E) is SEL—magic then q ≡ 0, 3(mod4). e minimum vertex degree δ of any SEL—monograph is at most 3. ere are exactly three nontrivial regular graphs K2,K3 and K2 × K3 which are SEL—magic. e define level joined planar grid graph L J : P m × P n and prove that it is SEL—magic. Also we give a general method of constructing new SEL—magic graphs from any given SEL—magic graph.