The number of walks in a graph

Dress A, Gutman I (2003)
Applied Mathematics Letters 16(5): 797-801.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Dress, AndreasUniBi; Gutman, Ivan
Abstract / Bemerkung
The aim of this note is to call attention to a simple regularity regarding the number of walks in a finite graph G. Let W-k denote the number of walks of length k(greater than or equal to 0) in G. Then W-a+b(2) less than or equal to W2aW2b holds for all a, b is an element of N-o while equality holds exclusively either (I) for all a, b is an element of N-o (in case G is a regular graph), or (II) for all a, b is an element of N, or (III) for all a, b is an element of N-o of equal parity (provided G is connected, this holds if and only if G is nonregular, yet semiregular graph), or (IV) for all a, b is an element of N of equal parity, or (V) just for a = b only. We show that all of these five cases can actually occur and discuss the resulting classification graphs in exactly five classes. (C) 2003 Elsevier Science Ltd. AN rights reserved.
Stichworte
eigenvectors (of graphs); regular graphs; semiregular graphs; harmonic; graphs; semiharmonic graphs; eigenvalues (of graphs); walks in graphs; spectral graph theory
Erscheinungsjahr
2003
Zeitschriftentitel
Applied Mathematics Letters
Band
16
Ausgabe
5
Seite(n)
797-801
ISSN
0893-9659
Page URI
https://pub.uni-bielefeld.de/record/1611240

Zitieren

Dress A, Gutman I. The number of walks in a graph. Applied Mathematics Letters. 2003;16(5):797-801.
Dress, A., & Gutman, I. (2003). The number of walks in a graph. Applied Mathematics Letters, 16(5), 797-801. https://doi.org/10.1016/S0893-9659(03)00085-5
Dress, A., and Gutman, I. (2003). The number of walks in a graph. Applied Mathematics Letters 16, 797-801.
Dress, A., & Gutman, I., 2003. The number of walks in a graph. Applied Mathematics Letters, 16(5), p 797-801.
A. Dress and I. Gutman, “The number of walks in a graph”, Applied Mathematics Letters, vol. 16, 2003, pp. 797-801.
Dress, A., Gutman, I.: The number of walks in a graph. Applied Mathematics Letters. 16, 797-801 (2003).
Dress, Andreas, and Gutman, Ivan. “The number of walks in a graph”. Applied Mathematics Letters 16.5 (2003): 797-801.

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