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Comparison of metrics on three-dimensional Lie groups

Federico G. Lastaria — 1991

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study local equivalence of left-invariant metrics with the same curvature on Lie groups G and G ¯ of dimension three, when G is unimodular and G ¯ is non-unimodular.

Adjacent vertex distinguishing edge colorings of the direct product of a regular graph by a path or a cycle

Laura Frigerio;  Federico Lastaria;  Norma Zagaglia Salvi — 2011

Discussiones Mathematicae Graph Theory

In this paper we investigate the minimum number of colors required for a proper edge coloring of a finite, undirected, regular graph G in which no two adjacent vertices are incident to edges colored with the same set of colors. In particular, we study this parameter in relation to the direct product of G by a path or a cycle.

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