Pell graceful labeling of graphs
Authors :
D. Muthuramakrishnan 1 * and S. Sutha 2
Author Address :
1,2 Department of Mathematics, National College, Trichy-620001, Tamil Nadu, India.
*Corresponding author.
Abstract :
In this paper, we introduce a new concept of Pell graceful labeling as follows. An injective function $f$ from $V(G)$ into $\{0, 1, 2, ..., p_q\}$ is Pell graceful if the induced edge labeling $f^{*}(uv)=|f(u)-f(v)|$ is a bijection onto the set $\{p_1, p_2, ..., p_q\}$. A graph $G(p, q)$ which admits a Pell graceful labeling is called a Pell graceful graph, where $p_q$ is the $q^{th}$ Pell number in the Pell sequence. Here, Pell graceful labeling of some family of graphs are obtained. Its non-existence are established.
Keywords :
Pell sequence, Pell graceful labeling, Pell graceful graph.
DOI :
Article Info :
Received : April 02, 2019; Accepted : July 11, 2019.
