Structure Fault Tolerance of Fully Connected Cubic Networks

Eminjan Sabir and Cheng-Kuan Lin ()
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Eminjan Sabir: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Cheng-Kuan Lin: Department of Computer Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan

Mathematics, 2025, vol. 13, issue 9, 1-13

Abstract: An interconnection network is usually modeled by a graph, and fault tolerance of the interconnection network is often measured by connectivity of the graph. Given a connected subgraph L of a graph G and non-negative integer t , the t -extra connectivity κ t ( G ) , the L -structure connectivity κ ( G ; L ) and the t -extra L -structure connectivity κ g ( G ; L ) of G can provide new metrics to measure the fault tolerance of a network represented by G . Fully connected cubic networks FC n are a class of hierarchical networks which enjoy the strengths of a constant vertex degree and good expansibility. In this paper, we determine κ t ( FC n ) , κ ( FC n ; L ) and κ t ( FC n ; L ) for t = 1 and L ∈ { K 1 , 1 , K 1 , 2 , K 1 , 3 } . We also establish the edge versions λ t ( FC n ) , λ ( FC n ; L ) and λ t ( FC n ; L ) for t = 1 and L ∈ { K 1 , 1 , K 1 , 2 } .

Keywords: connectivity; extra connectivity; structure connectivity; fully connected cubic networks; fault tolerance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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