On Strong, Ideal and Weak Super Magic Graphs

摘要

A graph G, where |V (G)| = p and |E(G)| = q, is called super magic if there exists a bijection f from V (G) [ E(G) to {1, 2, 3, ..., p + q} such that f(a) + f(b) + f(ab) = c'(f) is a constant for any ab 2 E(G), f(E(G)) = {1, 2, 3, ..., q} and f(V (G)) = {q+1, q+2, q+3, ..., p+q}. The super magic strength of a graph G is defined as the minimum of all c'(f) and is denoted by sms(G). This article gives bounds for super magic strength of some cycle-related graphs involving two parameters are given and the exact values of sms of some cycle-related graphs involving two parameters are obtained. Moreover, if SMS is the set of all super magic graphs, then we can decompose SMS into 3 partite sets, which are strong, ideal and weak super magic, respectively. We categorize several interesting graphs, some of them involving two parameters, into these partite sets.