English

Component edge connectivity of the folded hypercube

Combinatorics 2018-03-06 v1

Abstract

The gg-component edge connectivity cλg(G)c\lambda_g(G) of a non-complete graph GG is the minimum number of edges whose deletion results in a graph with at least gg components. In this paper, we determine the component edge connectivity of the folded hypercube cλg+1(FQn)=(n+1)g(i=0sti2ti1+i=0si2ti)c\lambda_{g+1}(FQ_{n})=(n+1)g-(\sum\limits_{i=0}^{s}t_i2^{t_i-1}+\sum\limits_{i=0}^{s} i\cdot 2^{t_i}) for g2[n+12]g\leq 2^{[\frac{n+1}2]} and n5n\geq 5, where gg be a positive integer and g=i=0s2tig=\sum\limits_{i=0}^{s}2^{t_i} be the decomposition of gg such that t0=[log2g],t_0=[\log_{2}{g}], and ti=[log2(gr=0i12tr)]t_i=[\log_2({g-\sum\limits_{r=0}^{i-1}2^{t_r}})] for i1i\geq 1.

Keywords

Cite

@article{arxiv.1803.01312,
  title  = {Component edge connectivity of the folded hypercube},
  author = {Shuli Zhao and Weihua Yang},
  journal= {arXiv preprint arXiv:1803.01312},
  year   = {2018}
}

Comments

The work was included in the MS thesis of the first author in [On the component connectiviy of hypercubes and folded hypercubes, MS Thesis at Taiyuan University of Technology, 2017]

R2 v1 2026-06-23T00:41:19.254Z