(1, N)-arithmetic graphs

被引：0

作者：

Ramachandran V. ^{[1
]}

Sekar C. ^{[2
]}

机构：

[1] Department of Mathematics, P.S.R Engineering College, Sivakasi

[2] Department of Mathematics, Aditanar College of Arts and Science, Tiruchendur

来源：

International Journal of Computers and Applications | 2016年 / 38卷 / 01期

关键词：

Arithmetic graph; C4k+2; cycle C4k; odd cycle and (1; N);

D O I：

10.1080/1206212X.2016.1218240

中图分类号：

O144 [集合论]; O157 [组合数学（组合学）];

学科分类号：

070104 ;

摘要：

A (p, q)-graph G is said to be (1, N)-arithmetic if there is a function Φ from the vertex set V(G) to {0, 1, N, (N + 1), 2N, (2N + 1), . . . , N(q - 1), N(q - 1) + 1} so that the values obtained as the sums of the labeling assigned to their end vertices, can be arranged in the arithmetic progression {1, N + 1, 2N + 1, . . . , N(q - 1) + 1}. In this paper, we prove that Stars, Paths, complete bipartite graph Km,n, highly irregular graph Hi(m,m) and Cycle C4k are (1, N)-arithmetic,C4k+2 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. © 2016 Informa UK Limited.

引用

页码：55 / 59

页数：4

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