k-Zumkeller graphs through mycielski transformation

Let G = (V, E) be a simple graph. A 1-1 function f : V → ℕ , where ℕ is the set of natural numbers, is said to induce a k-Zumkeller graph G if the induced edge function f * : E → ℕ defined by f* (xy) = f (x) f (y) satisfies the following conditions: (i) f* (xy) is a Zumkeller number for every xy ∈ E...

Full description

Saved in:
Bibliographic Details
Published inJournal of intelligent & fuzzy systems Vol. 46; no. 4; p. 7923
Main Authors Kalaimathi, M, Balamurugan, B J, Nagar, Atulya K
Format Journal Article
LanguageEnglish
Published London Sage Publications Ltd 18.04.2024
Subjects
Apexes
Graph theory
Graphs
Number theory
Online AccessGet full text
ISSN1064-1246
1875-8967
DOI10.3233/JIFS-231095

Cover

More Information
Summary:Let G = (V, E) be a simple graph. A 1-1 function f : V → ℕ , where ℕ is the set of natural numbers, is said to induce a k-Zumkeller graph G if the induced edge function f * : E → ℕ defined by f* (xy) = f (x) f (y) satisfies the following conditions: (i) f* (xy) is a Zumkeller number for every xy ∈ E. (ii) The total number of distinct Zumkeller numbers on the edges of G is k. A Mycielski transformation of a graph is a larger graph having more vertices and edges. In this article, the Mycielski transformation of a graphs such as path, cycle and star graphs have been computed and their k-Zumkeller graphs have been investigated by reducing the number of distinct Zumkeller numbers. AMS Subject Classification: 05C78
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1064-1246
1875-8967
DOI:10.3233/JIFS-231095