【作者】 彭锦； 李炜；

【Author】 PENG Jin LI Wei Department of Mathematical Science, Tsinghua University, Beijing 100084E-mail: jpeng@orsc.edu.cn Department of Mathematics, Huanggang Teachers College, Huanggang 438000

【机构】 清华大学教学科学系； 黄冈师范学院数学系；

【摘要】 具有p个顶点和q条边的简单图G=(V,E)称为边优美图,如果存在一个双射f:E→{1,2,…,q}使得诱导映射f~+:V→{0,1,…,p-1)也是一个双射,其中f~+(v)=sum from uv∈E to (f(uv))(mod p)。本文主要证明:卡氏积图C_m×C_n为边优美图的充分必要条件是uv∈Em和n皆为奇数。更多还原

【Abstract】 A graph G = (V, E) with p vertices and q edges is said to be edge-graceful if there exists a bijective mapping f : E - {1,2,... ,q} such that the induced mapping f+ : V -{0,1, ...,p - 1} defined by f+(v) = f(uv) (mod p) is also a bijection. In thispaper, we prove that the Cartesian product Cm x Cn is edge-graceful if and only if m and n are odd integers.更多还原