Name
Abstract | ||
|---|---|---|
For a positive integer k, let Z(k) = (Z(k), +, 0) be the additive group of congruences modulo k with identity 0, and Z(k) is the usual group of integers Z when k = 1. We call a finite simple graph G = (V(G), E(G)) to be Z(k)-magic if it admits an edge labeling l : E(G) -> Z(k) \ {0} such that the induced vertex sum labeling l(+) : V(G) -> Zk defined by l(+)(v) = Sigma(uv is an element of E(G)) (l(uv)) is constant. The constant is called a magic sum index, or an index for short, of G under the labeling l, which follows R. Stanley. The null set of G, which is defined by E. Salehi as the set of all k such that G is Z(k)-magic with zero magic sum index, and is denoted by Null(G). For fix integer k, we consider the set of all possible magic sum indices r such that G is Z(k)-magic with a magic sum index r, and denote it by I-k(G). We call I(k)(()G) the index set of G with respect to Z(k). In this paper, we investigate the properties and relations of the index sets I-k (C) and the null sets Null(G) for Z(k)-magic graphs. Among others, we determine the null sets of generalized wheels and generalized fans, and also construct infinitely many examples of Z(k)-magic graphs with magic sum zero. Some open problems are presented. |
Year | Venue | Keywords |
|---|---|---|
2015 | ARS COMBINATORIA | Z(k)-magic,magic sum index,null set,index set |
Field | DocType | Volume |
Integer,Graph,Discrete mathematics,Magic star,Combinatorics,Magic constant,Magic (paranormal),Mathematics | Journal | 118 |
ISSN | Citations | PageRank |
0381-7032 | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chia-Ming Lin | 1 | 0 | 0.34 |
| Tao-Ming Wang | 2 | 59 | 12.79 |