SUPER FIBONACCI GRACEFUL LABELING FOR GENERALIZED (a,m)-SHELL GRAPH AND MERGED WITH SOME GRAPHS

D. Senthil Kumar

  DOI:  https://doi.org/10.37418/amsj.9.11.91

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A graph $G$ with $p$ vertices and $q$ edges has super Fibonacci graceful labeling if there exists an injective map $f : V(G) \rightarrow \left\{F_{0}, F_{1},F_{2},\ldots F_{q}\right\}$ where $F_{k}$ is the $k^{th}$ Fibonacci number of the Fibonacci series such that its induced map $f^{+}: E(G) \rightarrow\left\{F_{1},F_{2},F_{3},\ldots F_{q}\right\}$  defined by $f^{+}(xy)$ =$\left|f(x) – f(y)\right|$ $\forall$ $xy \in G,$ is a bijective map.  In this paper, we investigate the existence of super Fibonacci graceful labeling for the various types of $(a, m)$ – shell graph and  $(a, m)$ – shell graph merged with some graphs.

Keywords: Graceful graph, Fibonacci graceful graph, super Fibonacci graceful graph, shell graph, (a,m)-shell graphs.