A totally magic cordial labeling of one-point union of n copies of a graph

Abstract. A graph \(G\) is said to have a totally magic cordial (TMC) labeling with constant \(C\) if there exists a mapping \(f: V(G)\cup E(G)\rightarrow \left\{0,1\right\}\) such that \(f(a) + f(b) + f(ab) \equiv C(\mbox{mod 2})\) for all \(ab\in E(G)\) and \(\left|n_f(0)-n_f(1)\right|\leq1\), where \(n_f(i)\) \((i = 0, 1)\) is the sum of the number of vertices and edges with label \(i\). In this paper, we establish the totally magic cordial labeling of one-point union of \(n\)-copies of cycles, complete graphs and wheels.