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arXiv · 2012.04020

$λ$-Core Distance Partitions

Xandru Mifsud
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Abstract

The $λ$-core vertices of a graph correspond to the non-zero entries of some eigenvector of $λ$ for a universal adjacency matrix $\mathbf{U}$ of the graph. We define a partition of the vertex set $V$ based on the $λ$-core vertex set and its neighbourhoods at a distance $r$, and give a number of results relating the structure of the graph to this partition. For such partitions, we also define an entropic measure for the information content of a graph, related to every distinct eigenvalue $λ$ of $\mathbf{U}$, and discuss its properties and potential applications.

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Xandru Mifsud. 2020-12-22. $λ$-Core Distance Partitions. https://doi.org/10.1016/j.laa.2020.12.012

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