On Regular Graphs and the Associated Real Algebras Generated by the Adjacency Matrices

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概要

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• We will observe the relations between regular graphs and the eigenvalues of the adjacencdy matrices. The number of eigenvalues is equal to the dimension of the real algebra generated by the adjacency matrix provided that the multiplicity of the valency is 1 and no eigenvalue is 0. (cf. Th. 1 and Cor. 1). It is known that a regular graph with 3-demensional associated algebra is strongly regular and this algebra is so-called centralizer algebra which means that a suitable basis of the algebra makes the edge set an association scheme (cf. [2]). We will introduce the concept of quasi strongly regular graph and show its associated algebra is a centraliazer algebra.

著者

• KOYAMA Toshiko

  Department of Pathology Saitama Social Insurance Hospital

• Koyama Toshiko

  Department Of Information Sciences Faculty Of Science Ochanomizu University

• Asamoto Noriko

  Department of Mathematics, Faculty of Science Ochanomizu University

• Uchibe Konagi

  Central Research Laboratory, Hitachi, Ltd.

• Uchibe Konagi

  Central Research Laboratory Hitachi Ltd.

• Asamoto Noriko

  Department Of Information Sciences Faculty Of Science Ochanomizu University

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