Cochin, India: Notes from a Nerve of the World

Joseph, M. K.

doi:10.1002/ad.177

Cited by 1 publication

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“…The results of Theorem 4.1 ( [12,Theorem 3.4]) are related to well-known results coming from Graph Theory for finite graphs. As far as we know, nilpotency on infinite locally-finite digraphs has been studied by [18], see also [17], so our approach may be useful to extend results in that direction as well. Proof.…”

Section: Nilpotencymentioning

confidence: 99%

The connection between evolution algebras, random walks and graphs

2019

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Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov chains. The winning of this relation is that many results coming from Probability Theory may be stated in the context of Abstract Algebra. In this paper we explore the connection between evolution algebras, random walks and graphs. More precisely, we study the relationships between the evolution algebra induced by a random walk on a graph and the evolution algebra determined by the same graph. Given that any Markov chain may be seen as a random walk on a graph we believe that our results may add a new landscape in the study of Markov evolution algebras. ∞ k=1 c ik = 1,for any i, k, then A is called Markov evolution algebra. The name is due to that there is an interesting one-to-one correspondence between A and a discrete time Markov chain (X n ) n≥0 with 2010 Mathematics Subject Classification. 05C25, 17D92, 17D99, 05C81.

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Section: Nilpotencymentioning

confidence: 99%