Browsing by Author "Elphick, Clive"

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A (FORGOTTEN) UPPER BOUND FOR THE SPECTRAL RADIUS OF A GRAPH
(2015-12)
Elphick, Clive
;
Liu, Chia-An
;
應用數學系
;
Department of Applied Mathematics
The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating from 1983 is equivalent to their much more recent bound. This bound is then used to compare lower bounds for the clique number. A series of line graph degree-based upper bounds for the Q-index is then proposed and compared experimentally with a graph based bound. Finally a new lower bound for generalised r-partite graphs is proved, by extending a result due to Erdos.
A (FORGOTTEN) UPPER BOUND FOR THE SPECTRAL RADIUS OF A GRAPH
(2015-12-01)
Elphick, Clive
;
Liu, Chia-An
;
應用數學系
;
Department of Applied Mathematics
The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating from 1983 is equivalent to their much more recent bound. This bound is then used to compare lower bounds for the clique number. A series of line graph degree-based upper bounds for the Q-index is then proposed and compared experimentally with a graph based bound. Finally a new lower bound for generalised r-partite graphs is proved, by extending a result due to Erdos.