Structure Fault Tolerance of Fully Connected Cubic Networks

Sabir, Eminjan; Lin, Cheng-Kuan

doi:10.3390/math13091532

Open AccessArticle

Structure Fault Tolerance of Fully Connected Cubic Networks

by

Eminjan Sabir

^1,† and

Cheng-Kuan Lin

^2,*,†

¹

College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

²

Department of Computer Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2025, 13(9), 1532; https://doi.org/10.3390/math13091532

Submission received: 27 February 2025 / Revised: 1 May 2025 / Accepted: 3 May 2025 / Published: 7 May 2025

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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 \in {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 \in {K_{1, 1}, K_{1, 2}}

.

Keywords: connectivity; extra connectivity; structure connectivity; fully connected cubic networks; fault tolerance

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MDPI and ACS Style

Sabir, E.; Lin, C.-K. Structure Fault Tolerance of Fully Connected Cubic Networks. Mathematics 2025, 13, 1532. https://doi.org/10.3390/math13091532

AMA Style

Sabir E, Lin C-K. Structure Fault Tolerance of Fully Connected Cubic Networks. Mathematics. 2025; 13(9):1532. https://doi.org/10.3390/math13091532

Chicago/Turabian Style

Sabir, Eminjan, and Cheng-Kuan Lin. 2025. "Structure Fault Tolerance of Fully Connected Cubic Networks" Mathematics 13, no. 9: 1532. https://doi.org/10.3390/math13091532

APA Style

Sabir, E., & Lin, C.-K. (2025). Structure Fault Tolerance of Fully Connected Cubic Networks. Mathematics, 13(9), 1532. https://doi.org/10.3390/math13091532

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Structure Fault Tolerance of Fully Connected Cubic Networks

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