(1, N)-arithmetic graphs
(1, N)-arithmetic graphs
复制标题
(1, N)-算术图
DOI：
10.1080/1206212x.2016.1218240
复制
发表时间：
2016
影响因子：
--
通讯作者：
C. Sekar
中科院分区：
文献类型：
--
作者：
V. Ramachandran;C. Sekar
一个（p，q）-图G称为（1，N）-算术的，如果存在一个从顶点集V（G）到的函数，使得作为赋给它们的端点的标号之和而得到的值可以排列在算术级数中。本文证明了星、路、完全二部图、高度不规则图和圈是（1，N）-算术的，不是（1，N）-算术的。我们还证明了对任意正整数N，不存在含奇圈的图G是（1，N）-算术图。
A (p, q)-graph G is said to be (1, N)-arithmetic if there is a function from the vertex set V(G) to so that the values obtained as the sums of the labeling assigned to their end vertices, can be arranged in the arithmetic progression . In this paper, we prove that Stars, Paths, complete bipartite graph , highly irregular graph and Cycle are (1, N)-arithmetic, is not (1, N)-arithmetic. We also prove that no graph G containing an odd cycle is (1, N)-arithmetic for every positive integer N.