On Fibonacci Range Labeling for Standard Shell Graphs
Aronthung S. Odyuo *
Department of Mathematics, St Joseph University, Ikishe Model Village, Chumukedima, Nagaland, India.
P. Mercy
Department of Mathematics, St Joseph University, Ikishe Model Village, Chumukedima, Nagaland, India.
*Author to whom correspondence should be addressed.
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.
Keywords: Shell graph, Fibonacci range labelling, Fibonacci range graph, golden ratio