A Note on the Order of Iterated Line Digraphs

Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices nk of the k‐iterated line digraph Lk(G), for k≥0, where L0(G)=G. We obtain this result by using the minimal polynomial of a quotient digraph π(G) of G.

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Vydané v:	Journal of graph theory Ročník 85; číslo 2; s. 395 - 399
Hlavní autori:	Dalfó, C., Fiol, M. A.
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	Hoboken Wiley Subscription Services, Inc 01.06.2017 Wiley
Predmet:	05 Combinatorics 05C Graph theory 05C20 05C50 adjacency matrix Classificació AMS Graph theory Line digraph Matemàtica discreta Matemàtiques i estadística minimal polynomial quotient digraph recurrence regular partition Teoria de grafs Àrees temàtiques de la UPC
ISSN:	0364-9024, 1097-0118
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Popis
Shrnutí:	Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices nk of the k‐iterated line digraph Lk(G), for k≥0, where L0(G)=G. We obtain this result by using the minimal polynomial of a quotient digraph π(G) of G.
Bibliografia:	Catalan Research Council and contract grant number: 2014SGR1147. Contract grant sponsor Ministerio de Economía y Competitividad contract grant number: MTM2014‐60127‐P; contract grant sponsor European Regional Development Fund ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0364-9024 1097-0118
DOI:	10.1002/jgt.22068