LACEABILITY PROPERTIES IN EDGE-TOLERANT TOTAL TRANSFORMATION GRAPHS $G^{\alpha \beta \gamma}$

Abstract

A bipartite graph $G$ is hamiltonian laceable if there is a hamiltonian path between any two vertices of $G$ from distinct vertex bipartite sets. A bipartite graph $G$ is $k$-edge fault-tolerant hamiltonian laceable if $G-F$ is hamiltonian laceable for every $F \subseteq E(G)$ with $|F| \leq k$. A graph $G$ is $k$-edge fault-tolerant conditional hamiltonian if $G-F$ is hamiltonian for every $F \subseteq E(G)$ with $|F| \leq k$ and $\delta(G-F) \geq 2$. In this paper, we establish laceability properties in the edge tolerant total transformation graphs $G^{\alpha \beta \gamma}$.