Loading...

Imprimitivity index of the adjacency matrix of digraphs

Akbari, S ; Sharif University of Technology | 2017

479 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2016.12.004
  3. Publisher: Elsevier Inc , 2017
  4. Abstract:
  5. Let G be a graph. An edge orientation of G is called smooth if the in-degree and the out-degree of every vertex differ by at most one. In this paper, we show that if G is a 2-edge-connected non-bipartite graph with δ(G)≥3, then G has a smooth primitive orientation. Among other results, using the spectral radius of digraphs, we show that if D1 is a primitive regular orientation and D2 is a non-regular orientation of a given graph, then for sufficiently large t, the number of closed walks of length t in D1 is more than the number of closed walks of length t in D2. © 2016 Elsevier Inc
  6. Keywords:
  7. Primitive digraph ; Spectral radius ; Directed graphs ; Graph theory ; Adjacency matrices ; Bipartite graphs ; Edge orientations ; Imprimitivity index ; In-Degree ; Number of closed walks ; Primitive digraphs ; Spectral radius ; Matrix algebra
  8. Source: Linear Algebra and Its Applications ; Volume 517 , 2017 , Pages 1-10 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0024379516305833