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Graph homomorphisms and nodal domains. (English) Zbl 1104.05044
Summary: We derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher’s inequality for $G$-designs.

05C50Graphs and linear algebra
Full Text: DOI
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