On super edge-magic deficiency of certain Toeplitz graphs

Abstract

A graph G is called edge-magic if there exists a bijective function φ : V (G) ∪ E(G) → {1, 2,. .. , |V (G)| + |E(G)|} such that φ(x) + φ(xy) + φ(y) = c(φ) is a constant for every edge xy ∈ E(G), called the valence of φ. Moreover, G is said to be super edge-magic if φ(V (G)) = {1, 2,. .. , |V (G)|}. The super edge-magic deciency of a graph G, denoted by µs(G), is the minimum nonnegative integer n such that G ∪ nK1, has a super edge-magic labeling, if such integer does not exist we dene µs(G) to be +∞. In this paper, we study the super edge-magic deciency of some Toeplitz graphs.

On the super edge-magic deficiency of join product and chain graphs

“…Ngurah et al [11,12] studied the super edge-magic deficiency of some classes of chain graphs, wheels, fans, double fans, and disjoint union of particular type of complete bipartite graphs. Recently, Ahmad and Muntaner-Battle [2] studied the super edge-magic deficiency of several classes of unicyclic graphs. The authors refer the reader to the survey paper by Gallian [9] for some of the latest developments in these and other types of graph labelings.…”

Super edge-magic labeling of graphs: deficiency and maximality

“…The super edge-magic deficiency of complete bipartite graphs K m,n and disjoin union of stars are investigated in [10]. The super edgemagic deficiency of some classes of unicyclic graphs are studied in [1,2] . The latest developments in these and other types of graph labelings can be found in [9].…”