Characterization of certain families of modular multiplicative divisor graphs

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 ce...

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Bibliographic Details
Published in:Journal of Taibah University for Science Vol. 11; no. 2; pp. 294 - 297
Main Authors: Revathi, R., Ganesh, S.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2017
Taylor & Francis Group
Subjects:
Arbitrary supersubdivision
Cyclic decomposition
Graph labelling
graphs
Cyclic decomposition
Arbitrary supersubdivision
Graph labelling
ISSN:1658-3655, 1658-3655
Online Access:Get full text
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Summary: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.
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ISSN:1658-3655
1658-3655
DOI:10.1016/j.jtusci.2015.09.004