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Abstract:
For 0 <=alpha< 1 and ak-uniform hypergraphH, the tensorA(alpha)(H) associated withHis defined asA(alpha)(H) =alpha D(H) + (1- alpha)A(H), whereD(Script capital H) andA(H) are the diagonal tensor of degrees and the adjacency tensor ofH, respectively. The alpha-spectra ofHis the set of all eigenvalues ofA(alpha)(H) and the alpha-spectral radius rho(alpha)(H) is the largest modulus of the elements in the spectrum ofA(alpha)(H). In this paper we define the line graphL(H) of a uniform hypergraphHand prove that rho alpha(H)<= 1 kappa rho alpha(L(H))+1+alpha(Delta-1-delta*k), where Delta and delta* are the maximum degree ofHand the minimum degree ofL(H), respectively. We also generalize some results on alpha-spectra ofG(k,s), which is obtained fromGby blowing up each vertex into ans-set and each edge into ak-set where 1 <= s <= k/2.
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ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN: 1439-8516
CN: 11-2039/O1
Year: 2020
Issue: 7
Volume: 36
Page: 842-850
0 . 9 5 5
JCR@2020
0 . 8 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:50
JCR Journal Grade:3
CAS Journal Grade:3
Cited Count:
WoS CC Cited Count: 2
SCOPUS Cited Count: 2
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 0