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- W2762650339 abstract "The parameter $sigma(G)$ of a graph $G$ stands for the number of Laplacian eigenvalues greater than or equal to the average degree of $G$. In this work, we address the problem of characterizing those graphs $G$ having $sigma(G)=1$. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between $sigma(G)$ and the number of anticomponents of $G$. As a by-product, we present some results which support the conjecture, by restricting our analysis to some classes of graphs." @default.
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- W2762650339 date "2017-10-04" @default.
- W2762650339 modified "2023-09-27" @default.
- W2762650339 title "Partial characterization of graphs having a single large Laplacian eigenvalue" @default.
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