๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The set of generalized exponents of primitive simple graphs

โœ Scribed by Jia-Yu Shao; Bin Li

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
979 KB
Volume
258
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

โœฆ Synopsis

The exponent of a primitive digraph is the smallest integer k such that for each ordered pair of (not necessarily distinct) vertices x and y there is a walk of length k from x to y. The exponent set (the set of those numbers attainable as exponents of primitive digraphs with n vertices) and bounds on the exponent have been extensively studied. As a generalization of exponent, R. A. Brualdi and B. Liu introduced three types of generalized exponents for primitive digraphs in 1990. We improve the bounds on these generalized exponents given by B. Liu for primitive simple graphs, and we express explicitly for this class of primitive graphs the exponent sets of all three types of generalized exponents.

๐Ÿ“œ SIMILAR VOLUMES

Generalized exponents of primitive direc
Generalized exponents of primitive directed graphs
โœ Richard A. Brualdi; Bolian Liu ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 655 KB

## Abstract The exponent of a primitive digraph is the smallest integer __t__ such that for each ordered pair of (not necessarily distinct) vertices __x__ and __y__ there is a path of length __t__ from __x__ to __y__. There is considerable information known about bounds on exponents and those numbe

Generalized exponents of primitive symme
Generalized exponents of primitive symmetric digraphs
โœ Richard A. Brualdi; Shao Jia-yu ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 1014 KB

A strongly connected digraph D of order n is primitive (aperiodic) provided the greatest common divisor of its directed cycle lengths equals 1. For such a digraph there is a minimum integer t, called the exponent of D, such that given any ordered pair of vertices x and y there is a directed walk fro