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Associating hub‐directed multigraphs to arrowhead matrices
Author(s) -
Marrero J. Abderramán,
Valdés Juan Núñez,
Villar María Trinidad
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4336
Subject(s) - multigraph , adjacency matrix , directed graph , combinatorics , adjacency list , mathematics , graph , graph theory , matrix (chemical analysis) , class (philosophy) , discrete mathematics , computer science , artificial intelligence , chemistry , chromatography
In this paper, we use the arrowhead matrices as a tool to study graph theory. More precisely, we deal with an interesting class of directed multigraphs, the hub‐directed multigraphs. We associate the arrowhead matrices with the adjacency matrices of a class of directed multigraph, and we obtain new properties of the second objects by using properties of the first ones. The hub‐directed multigraphs with potential use in applications are also defined. As main result, we show that a hub‐directed multigraph G ( H ) with adjacency matrix H ∗ is a dominant hub‐directed multigraph if and only if H ∗ = C E , where C is the adjacency matrix of another directed multigraph and E is the adjacency matrix of a particular elementary dominant hub‐directed pseudo‐graph. Another decomposition of its Gram (arrowhead) matrix A =H ∗TH ∗is also given. Copyright © 2017 John Wiley & Sons, Ltd.