Simple digraph analogue of Brualdi-Hoffman-conjecture
碩士 === 國立交通大學 === 應用數學系所 === 107 === An arc ab is single-direction if ba is not an arc in a digraph. Let e be a positive integer. Then there is a unique pair (s,t) of integers such that e=s(s-1)+t, where s is positive and 0<=t<=2s-1. For 2s-7<=t<=2s-3 and t ̸=0,1, we prove that the maxim...
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| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2019
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| Online Access: | http://ndltd.ncl.edu.tw/handle/23h873 |
| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 107 === An arc ab is single-direction if ba is not an arc in a digraph. Let e be a positive integer. Then there is a unique pair (s,t) of integers such that e=s(s-1)+t,
where s is positive and 0<=t<=2s-1. For 2s-7<=t<=2s-3 and t ̸=0,1, we prove that the maximum spectral radius of a simple digraph D with e arcs and without isolated vertices is when D is obtained from complete digraph \overleftrightarrow{K_s} by adding a new
vertex x and t arcs, connecting x and ⌊t\2⌋ vertices in \overleftrightarrow{K_s} with at most one arc being single-direction.
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