Note on Group Distance Magic Graphs G[C 4]

被引：13

作者：

Cichacz, Sylwia ^{[1
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

来源：

GRAPHS AND COMBINATORICS | 2014年 / 30卷 / 03期

关键词：

Distance magic labeling; Magic constant; Sigma labeling; Graph labeling; Abelian group; Composition of graphs; Lexicographic product of graphs;

D O I：

10.1007/s00373-013-1294-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A group distance magic labeling or a -distance magic labeling of a graph G = (V, E) with is a bijection f from V to an Abelian group of order n such that the weight of every vertex is equal to the same element , called the magic constant. In this paper we will show that if G is a graph of order n = 2 (p) (2k + 1) for some natural numbers p, k such that for some constant c for any , then there exists a -distance magic labeling for any Abelian group of order 4n for the composition G[C (4)]. Moreover we prove that if is an arbitrary Abelian group of order 4n such that for some Abelian group of order n, then there exists a -distance magic labeling for any graph G[C (4)], where G is a graph of order n and n is an arbitrary natural number.

引用

页码：565 / 571

页数：7