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Research Article Open access CC BY 4.0

On Fibonacci Range Labeling for Standard Shell Graphs

Aronthung S. Odyuo, P. Mercy

Journal of Advances in Mathematics and Computer Science · pp. 67–75 · Published 24 Apr 2023

10.9734/jamcs/2023/v38i71773

Abstract

A shell C[n, (n - 3)] of size n is a graph obtained by taking (n - 3) concurrent chords in a cycle \(C_n\) on n vertices. Deb and Limaye (2002) have conjectured that all multiple shells are harmonious. The conjecture has prove to be true for uniform double shells, uniform triple shells and uniform quadruple shells. Here, we prove for a non- uniform double shells with order m and n, where n = (m - 1) and \(\kappa\)-copies of a shell C[n, (n - 3)]\(\kappa\) with a union of \(K_2\) for n = 4, 2\(K_2\) for n = 6 and 3\(K_2\) for n = 8, having a common end vertex joined to the apex of the shell are Fibonacci range labeling.

Shell graph Fibonacci range labelling Fibonacci range graph golden ratio

References (5)

  1. 1 A Dynamic Survey of Graph Labeling [DOI]
  2. 2 GRACEFUL NUMBERING OF WHEELS AND RELATED GRAPHS [DOI]
  3. 3 Graceful graphs : Some further results and problems.
  4. 4 Graceful Labeling of Bow Graphs and Shell-Flower Graphs [DOI]
  5. 5 All Uniform Bow Graphs are Graceful [DOI]

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