Rees semigroups of digraphs for classification of data

Abawajy, Jemal; Kelarev, AV; Miller, Mirka; Ryan, Jennifer K.

doi:10.1007/s00233-014-9685-x

Cited by 9 publications

(3 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are many different ways to associate a graph to the given group, including the commuting graphs [4], prime graphs [12], and of course Cayley graphs, which have a long history and applications [14]. Graphs associated with groups and other algebraic structures have been actively investigated since they have valuable applications [2,24,25] and specially are related to automata theory [15,16]. The rigorous development of the mathematical theory of complexity via algebraic automata theory reveals deep and unexpected connections between algebra (semigroups) and areas of science and engineering.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite groups with the same Power graph

Mirzargar¹,

Scapellato²

2020

Preprint

View full text Add to dashboard Cite

The power graph P (G) of a group G is a graph with vertex set G, where two vertices u and v are adjacent if and only if u = v and u m = v or v m = u for some positive integer m. In this paper, we raise and study the following question: For which natural numbers n every two groups of order n with isomorphic power graphs are isomorphic? In particular, we determine prove that all such n are cube-free and are not multiples of 16. Moreover, we show that if two finite groups have isomorphic power graphs and one of them is nilpotent or has a normal Hall subgroup, the same is true with the other one.

show abstract

Section: Introductionmentioning

confidence: 99%

“…For example, two groups of order 16 with the same numbers of elements of each order, e.g. C 4 × C 4 and C 2 × Q 8 are SmallGroup (16,2) and SmallGroup (16,4) in GAP respectively [10]. Their power graphs are not isomorphic.…”

Section: Introductionmentioning

confidence: 99%

Finite groups with the same Power graph

Mirzargar¹,

Scapellato²

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The investigation of ideals with largest weight has been motivated by applications of ideals in data mining (cf. [8,11,25]), health informatics (cf. [4,6,7,19,20,32]) and information security (cf.…”

Section: Introductionmentioning

confidence: 99%