English

Vertex and Mixed $k$-Diameter Component Connectivity

Combinatorics 2021-11-09 v1

Abstract

n the kk-diameter component connectivity model a network is consider operational if there is a component with diameter at least kk. Therefore, a network is in a failure state if every component has diameter less than kk. In this paper we find the vertex variant of the kk-diameter component connectivity parameter, which is the minimum number of vertex deletions in order to put a network into a failure state, for particular classes of graphs. We also show the mixed variant by allowing vertex and edge failures within the network. We show results for paths, cycles, complete, and complete bipartite graphs for both variants as well as perfect rr-ary trees for the vertex variant.

Keywords

Cite

@article{arxiv.2111.04262,
  title  = {Vertex and Mixed $k$-Diameter Component Connectivity},
  author = {Adam Buzzard and Nathan Shank},
  journal= {arXiv preprint arXiv:2111.04262},
  year   = {2021}
}

Comments

Revised version was accepted for publication in Mathematical Exchange

R2 v1 2026-06-24T07:29:53.211Z