On Fibonacci Range Labeling for Standard Shell Graphs

A shellC[n,(n−3)] of sizenis a graph obtained by taking (n−3) concurrent chords in a cycleCnonnvertices. Deb and Limaye (2002) have conjectured that all multiple shells are harmonious. The conjecturehas 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 ordermandn, wheren= (m−1) andk-copies of a shellC[n,(n−3)]kwith a union ofK2forn= 4, 2K2forn= 6 and 3K2forn= 8, having a common end vertexjoined to the apex of the shell are Fibonacci range labeling.