On the construction of new classes of super mean graphs
R. Vasuki, A. Nagarajan · Journal of Discrete Mathematical Sciences and Cryptography · 2010
Let G be a (p, q) graph and f : V(G) → {1, 2, 3,…, p + q} be an injection. For each edge e = uv, the induced edge labeling f* is defined as follows: Then f is called super mean labeling if f (V(G)) ∪ {f* (e) : e ∈ E(G)} = {1, 2, 3,…, p + q}. A graph that admits a super mean labeling is called super mean graph. In this paper, we discuss the construction of two kinds of super mean graphs. Here we prove that (Pm ; Cn )n ≥ 3 and n = 4, (P 2n ; Sm )m ≥ 1, n ≥ 1, [Pm ; Cn ]n ≥ 3 and n ≠ 4, [P 2n ; Sm ]m ≥ 1, n ≥ 1 and , m ≥ 1, n ≥ 3 and n ≠ 4 are super mean graphs. Also we establish that union of any number of super mean graph is a super mean graph.