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- W2963028288 abstract "Let $$Gamma $$ be a finite graph and let $$A(Gamma )$$ be its adjacency matrix. Then $$Gamma $$ is singular if $$A(Gamma )$$ is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. Here we investigate this problem for Cayley graphs $$mathrm{Cay}(G,H)$$ when G is a finite group and when the connecting set H is a union of conjugacy classes of G. In this situation, the singularity problem reduces to finding an irreducible character $$chi $$ of G for which $$sum _{hin H},chi (h)=0.$$ At this stage, we focus on the case when H is a single conjugacy class $$h^G$$ of G; in this case, the above equality is equivalent to $$chi (h)=0$$. Much is known in this situation, with essential information coming from the block theory of representations of finite groups. An element $$hin G$$ is called vanishing if $$chi (h)=0$$ for some irreducible character $$chi $$ of G. We study vanishing elements mainly in finite simple groups and in alternating groups in particular. We suggest some approaches for constructing singular Cayley graphs." @default.
- W2963028288 created "2019-07-30" @default.
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- W2963028288 date "2018-11-30" @default.
- W2963028288 modified "2023-09-24" @default.
- W2963028288 title "Remarks on singular Cayley graphs and vanishing elements of simple groups" @default.
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- W2963028288 doi "https://doi.org/10.1007/s10801-018-0860-0" @default.
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