394 research outputs found
Remarks on singular Cayley graphs and vanishing elements of simple groups
Let Γ be a finite graph and let A(Γ) be its adjacency matrix. Then Γ is singular if A(Γ) is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. Here we investigate this problem for Cayley graphs 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 χ of G for which ∑h∈Hχ(h)=0. At this stage, we focus on the case when H is a single conjugacy class hG of G; in this case, the above equality is equivalent to χ(h)=0 . Much is known in this situation, with essential information coming from the block theory of representations of finite groups. An element h∈G is called vanishing if χ(h)=0 for some irreducible character χ 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
Internationalisation and development in East Asian higher education: an introduction
It is important to recognise that comparison is not a method or even an academic technique; rather, it is a discursive strategy… Good comparisons often come from the experience of strangeness and absences. (Benedict Anderson, 2016
Calculations Predict That Carbon Tunneling Allows the Degenerate Cope Rearrangement of Semibullvalene to Occur Rapidly at Cryogenic Temperatures
Article on calculations predicting that carbon tunneling allows the degenerate cope rearrangement of semibullvalene to occur rapidly at cryogenic temperatures
Tuning Reactivity and Electronic Properties through Ligand Reorganization within a Cerium Heterobimetallic Framework
Mapping the Binding Site of a Large Set of Quinazoline Type EGF-R Inhibitors Using Molecular Field Analyses and Molecular Docking Studies
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