On the Integer-Magic Spectra of the Corona of Two Graphs

摘要

A graph G is said to be k-magic if there exists an edge labeling l : E(G) → Z_k~* such that the induced vertex labeling l~+ : V(G) → Z_k defined by l~+(v) = ∑_(uv∈E(G)) l(uv) is a constant map. We call the set of all k for which G is k-magic the integer-magic spectrum of G. The corona of G with another graph H is the graph consisting of one copy of G and | V(G)| copies of H, with new edges connecting the ith vertex of G to each vertex in the ith copy of H. In this paper, we investigate the integer-magic spectra of the coronas of some specific graphs including paths, cycles, complete graphs and stars.