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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Bibliographic Details
Published in:Journal of graph theory Vol. 85; no. 2; pp. 395 - 399
Main Authors: Dalfó, C., Fiol, M. A.
Format: Journal Article Publication
Language:English
Published: Hoboken Wiley Subscription Services, Inc 01.06.2017
Wiley
Subjects:
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
Online Access:Get full text
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Description
Summary: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.
Bibliography: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