The p-spectral radius of the Laplacian matrix
2018 ◽
Vol 12
(2)
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pp. 455-466
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The p-spectral radius of a graph G=(V,E) with adjacency matrix A is defined as ?(p)(G) = max||x||p=1 xT Ax. This parameter shows connections with graph invariants, and has been used to generalize some extremal problems. In this work, we define the p-spectral radius of the Laplacian matrix L as ?(p)(G) = max||x||p=1 xT Lx. We show that ?(p)(G) relates to invariants such as maximum degree and size of a maximum cut. We also show properties of ?(p)(G) as a function of p, and a upper bound on maxG: |V(G)|=n ?(p)(G) in terms of n = |V| for p > 2, which is attained if n is even.
2011 ◽
Vol 03
(02)
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pp. 185-191
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2019 ◽
Vol 35
(1)
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pp. 31-40
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