in this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. we present some sufficient and necessary conditions for $gbox h$ being hamilton-connected when $g$ is a hamilton-connected graph and $h$ is a tree or $g$ is a hamiltonian graph and $h$ is $k_2$.

Curran, S.J., Hamilton paths in Cayley digraphs of metacyclic groups, Discrete Mathematics 115 (1993) 133-139. We obtain a characterization of all Hamilton paths in the Cayley digraph of a metacyclic group G with generating set {x, y} where (yx-‘) a G. The abundance of these Hamilton paths allows us to show that Hamilton paths occur in groups of at least two.

conclusions considering the results of this study, lavandula angustifilia infusion has some positive therapeutic effects on depressed patients most importantly decreases mean depression score and might be used alone or as an adjunct to other anti-depressant drugs. results after four weeks of the trial onset, the mean depression score according to the hamilton scale for depression was 17.5 ± 3.5...