### Bibliography

Pranava K Jha, Naveen Agnihotri and Rajesh Kumar. 1997. Long
cycles and long paths in the Kronecker product of a cycle and a
tree. *Discrete Applied Mathematics*. **74**(2):101-121.
#### Abstract

Let *Cm × T* denote the Kronecker product of a cycle
*Cm* and a tree *T*. If *m* is odd, then
*Cm × T* is connected, otherwise this graph consists
of two isomorphic components. This paper presents a scheme which
constructs a long cycle in each component of *Cm × T*,
where *T* satisfies certain degree constraints. The cycle thus
traced is shown to be a dominating set, and in some cases, a vertex
cover of that component. The algorithm builds on *(i)* results
on longest cycles in *Cm × Pn*, where *Pn* is
a path on *n* vertices, and *(ii)* a path factorization
of *T*. Additional results include characterizations for the
existence of a Hamiltonian cycle and for that of a Hamiltonian path
in *Cm × T*.

*naveen@bhalu.com*