Some Indices of Alphabet Overlap Graph

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 = （v1...vk）; vi ∈ {1,2,... ,d}, i = 1,2,... ,k}...

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Bibliographic Details
Published inJournal of computer science and technology Vol. 27; no. 4; pp. 897 - 902
Main Author 杨荣 杨兆兰 张和平
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.07.2012
Springer Nature B.V
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China%Normal School, Gansu Lianhe University, Lanzhou 730000, China
Subjects
Alphabets
Apexes
Artificial Intelligence
Bruijn图
Communication networks
Communications networks
Computer Science
Computer simulation
Connectivity
Data Structures and Information Theory
Graph theory
Graphs
Information Systems Applications (incl.Internet)
Mathematical analysis
Mathematical models
Short Paper
Software Engineering
Studies
Theorems
Theory of Computation
Vertex sets
字母
连通性
通信网络
顶点度
顶点集
顶焦度
undirected de Bruijn graph
vertex degree
connectivity
alphabet overlap graph
Online AccessGet full text
ISSN1000-9000
1860-4749
1860-4749
DOI10.1007/s11390-012-1261-9

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Summary: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 = （v1...vk）; vi ∈ {1,2,... ,d}, i = 1,2,... ,k}; they are distinct and two vertices u = （ul...uk） and v = （vl... vk） are adjacent if and only if us＋i = vi or vs＋i = ui （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.
Bibliography:Rong Yang, Zhao-Lan Yang, He-Ping Zhang（1 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China ;2Normal School, Gansu Lianhe University, Lanzhou 730000, China）
11-2296/TP
undirected de Bruijn graph, alphabet overlap graph, vertex degree, connectivity
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 = （v1...vk）; vi ∈ {1,2,... ,d}, i = 1,2,... ,k}; they are distinct and two vertices u = （ul...uk） and v = （vl... vk） are adjacent if and only if us＋i = vi or vs＋i = ui （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.
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ISSN:1000-9000
1860-4749
1860-4749
DOI:10.1007/s11390-012-1261-9