(1,  N)-arithmetic graphs. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Ramachandran, V.; Sekar, C.
• Is Part Of: International journal of computers and applications. Volume 38:Issue 1(2016)
• Page Start: 55
• Page End: 59
• Publication Date: 2016-01-02
• Subjects: Arithmetic graph -- cycle -- -- odd cycle and (1 -- N); Computers -- Periodicals; Computer software -- Periodicals; Computer networks -- Periodicals; Multimedia systems -- Periodicals; Internet -- Periodicals; World Wide Web -- Periodicals; Minicomputers -- Periodicals; Microcomputers -- Periodicals; 004.05
• DOI: 10.1080/1206212X.2016.1218240
• Languages: English
• ISSNs: 1206-212X

Abstract

Abstract : 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 .