Abstract Title

Two-sided Cayley Graphs

Disciplines

Algebra | Mathematics

Abstract

Cayley graphs were introduced by Arthur Cayley in 1878 to geometrically describe the algebraic structure of a group. Due to their strong symmetry, Cayley graphs find application in molecular biology, physics, and computer science. In particular, they are used in modelling interconnection networks in parallel computing. We study a new class of graphs recently introduced by Iradmusa and Praeger called two-sided Cayley graphs. Since two-sided Cayley graphs are more general and can exhibit similar symmetry, they are likely to find similar applications. We present an overview of our ongoing research which includes results in connectivity and vertex-transitivity of two-sided Cayley graphs. Pictorial examples are included to illustrate the central ideas behind our findings.

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Two-sided Cayley Graphs

Cayley graphs were introduced by Arthur Cayley in 1878 to geometrically describe the algebraic structure of a group. Due to their strong symmetry, Cayley graphs find application in molecular biology, physics, and computer science. In particular, they are used in modelling interconnection networks in parallel computing. We study a new class of graphs recently introduced by Iradmusa and Praeger called two-sided Cayley graphs. Since two-sided Cayley graphs are more general and can exhibit similar symmetry, they are likely to find similar applications. We present an overview of our ongoing research which includes results in connectivity and vertex-transitivity of two-sided Cayley graphs. Pictorial examples are included to illustrate the central ideas behind our findings.