Characterization of certain families of modular multiplicative divisor graphs. Issue 2 (1st March 2017)

• Record Type: Journal Article
• Authors: Revathi, R.; Ganesh, S.
• Is Part Of: Journal of Taibah University for science. Volume 11:Issue 2(2017)
• Page Start: 294
• Page End: 297
• Publication Date: 2017-03-01
• Subjects: Graph labelling -- Arbitrary supersubdivision -- Cyclic decomposition; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1016/j.jtusci.2015.09.004
• Languages: English
• ISSNs: 1658-3655

Abstract

Abstract: A modular multiplicative divisor (MMD) labelling of a graph G with p vertices and q edges is a bijection f from the set of all vertices to the set of positive integers {1, 2, …, p } such that the sum of all edge labels f* ( uv ) = f ( u ) f ( v )( modp ); uv ∈ E ( G ) is a multiple of p . In this paper, we characterize certain classes of MMD graphs. This result is a solution to the open problem posed by G. Sethuraman in AKCE International Journal of Graphs and Combinatorics, No. 1 (2009) 229–236. In addition, we discuss the role of MMD labelling in obtaining cyclic decompositions of certain families of graphs into specific graphs.