Open AccessThe l-good-neighbor edge connectivity of graphs
Author(s) -
Shumin Zhang,
Yalan Li,
Chengfu Ye
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2132/1/012027
Subject(s) - combinatorics , enhanced data rates for gsm evolution , graph , mathematics , k nearest neighbors algorithm , connectivity , order (exchange) , discrete mathematics , computer science , artificial intelligence , finance , economics
The l -good-neighbor edge connectivity is an useful parameter to measure the reliability and tolerance of interconnection networks. For a graph H with order p and an integer l ( l ≥ 0), an edge subset X ⸦ E ( H ) is called a l -good-neighbor edge-cut if H − X is disconnected and the minimum degree of every component of H − X is at least £. The order of the minimum l -good-neighbor edge-cut of H is called the l -good-neighbor edge connectivity of H , denoted by λ l ( H ). In this paper, we show λ ( H ) ≤ λ l+1 ( H ), obtain the bounds of λ l ( H ) when 0 ≤ l ≤ [ p -2/2], character some graphs with the small λ l ( H ) and get some results about the Erdös-Gallai-type problem about λ l ( H ).