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A note on the invariant factors of the walk matrix of a graph
- Authors
- Choi, Jinwon; Moon, Sunyo; Park, Seungkook
- Issue Date
- 15-Dec-2021
- Publisher
- ELSEVIER SCIENCE INC
- Keywords
- Walk matrix; Invariant factors; Smith normal form
- Citation
- LINEAR ALGEBRA AND ITS APPLICATIONS, v.631, pp 362 - 378
- Pages
- 17
- Journal Title
- LINEAR ALGEBRA AND ITS APPLICATIONS
- Volume
- 631
- Start Page
- 362
- End Page
- 378
- ISSN
- 0024-3795
1873-1856
- Abstract
- For a given graph G with nvertices, the walk matrix Wof Gis defined as W=[e Ae A(2)e ... A(n-1)e], where A is the adjacency matrix of the graph Gand eis the vector of all ones. In this paper, we prove that for any positive integer k, at most left perpendicularn/2right perpendicular invariant factors of W are congruent to 2(k) modulo 2(k+1). (c) 2021 Elsevier Inc. All rights reserved.
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