Abstract
Tian and Meng in [Y. Tian and J. Meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regularity k and girth g(G) ≥ 6 is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree δ(G) ≥ 6 and girth g(G) ≥ 6.
Highlights
We show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree G 4 and girth g G 6
The traditional connectivity and edge-connectivity, are important measures for networks, which can correctly reflect the fault tolerance of systems with few processors, but it always underestimates the resilience of large networks
The discrepancy incurred is because events whose occurrence would disrupt a large network after a few processors, the disruption envisaged occurs in a worst case scenario
Summary
The traditional connectivity and edge-connectivity, are important measures for networks, which can correctly reflect the fault tolerance of systems with few processors, but it always underestimates the resilience of large networks. We show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree G 4 and girth g G 6 . A graph has a cyclic edge-cut if and only if it has two vertexdisjoint cycles.
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