LUCAS DECOMPOSITION OF GRAPHS

R. Hema, D. Subitha, and S. Freeda

  DOI:  https://doi.org/10.37418/amsj.9.11.103

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A decomposition $(G_{1}, G_{2} , \ldots , G_{n} )$ of $G$ is said to be Lucas Decomposition (LD) if (i) $q(G_{1}) = 2$, $q(G_{2}) = 1$, (ii) $q(G_{i}) = q(G_{i-1}) + q(G_{i-2})$, $i = 3, 4, \ldots , n $, (iii) $E(G ) = E(G_{1}) \cup E(G_{2}) \cup \ldots . \cup E(G_{n})$ (iv) Each $G_{i}$, $i = 1, 2, \ldots , n$ is connected. In this paper, we investigate Lucas Decomposition of some graphs.

Keywords: Decomposition, Lucas Decomposition, Lucas Star Decomposition.