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- W833973862 abstract "A graph G is said to be determined by its permanental spectrum if any graph having the same permanental spectrum as G is isomorphic to G. In this paper, we introduce the permanental nullity of a graph, the multiplicity of the number zero in the permanental spectrum of a graph, to study graphs determined by their permanental spectra. First, we determine all graphs of order n whose permanental nullities are n−2, n−3, n−4 and n−5, respectively. Then, we show that all graphs with the permanental nullity n−2, n−3, or n−5, and all non-bipartite graphs with the permanental nullity n−4 are determined by their permanental spectra. In particular, we prove that the complete bipartite graphs are determined by their permanental spectra." @default.
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- W833973862 date "2015-11-01" @default.
- W833973862 modified "2023-10-07" @default.
- W833973862 title "Per-spectral characterizations of graphs with extremal per-nullity" @default.
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- W833973862 doi "https://doi.org/10.1016/j.laa.2015.06.018" @default.
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