NDLI: Some Indices of Alphabet Overlap Graph

Content Provider	Springer Nature Link
Author	Yang, Rong Yang, Zhao Lan Zhang, He Ping
Copyright Year	2012
Abstract	The undirected de Bruijn graph is often used as the model of communication network for its useful properties, such as short diameter, small maximum vertex degree. In this paper, we consider the alphabet overlap graph G(k, d, s): the vertex set V = {v\|v = (v $_{1}$ …v $_{ k }$); v $_{ i }$ ∈ {1, 2,…, d}, i = 1, 2,…, k}; they are distinct and two vertices u = (u $_{1}$…u $_{ k }$) and v = (v $_{1}$…v $_{ k }$) are adjacent if and only if u $_{ s+i }$ = v $_{ i }$ or v $_{ s+i }$ = u $_{ i }$ (i = 1, 2,…, k − s). In particular, when s = 1, G(k, d, s) is just an undirected de Bruijn graph. First, we give a formula to calculate the vertex degree of G(k, d, s). Then, we use the corollary of Menger’s theorem to prove that the connectivity of G(k, d, s) is 2d $^{ s }$ − 2d $^{2s−k }$ for s ≥ k/2.
Starting Page	897
Ending Page	902
Page Count	6
File Format	PDF
ISSN	10009000
Journal	Journal of Computer Science and Technology
Volume Number	27
Issue Number	4
e-ISSN	18604749
Language	English
Publisher	Springer US
Publisher Date	2012-07-12
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	undirected de Bruijn graph alphabet overlap graph vertex degree connectivity Software Engineering Information Systems Applications (incl. Internet) Data Structures, Cryptology and Information Theory Theory of Computation Computer Science Artificial Intelligence (incl. Robotics)
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computer Science Applications Software Hardware and Architecture

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