<abstract xmlns="http://www.w3.org/1999/xhtml">The product graph <italic>Gm *Gp</italic> of two given graphs <italic>Gm</italic> and <italic>Gp</italic>, defined by J.C. Bermond et al.[J Combin Theory, Series B 36(1984) 32-48] in the context of the so-called (<italic>Δ,D</italic>)-problem, is one interesting model in the design of large reliable networks. This work deals with sufficient conditions that guarantee these product graphs to be hamiltonian-connected. Moreover, we state product graphs for which provide panconnectivity of interconnection networks modeled by a product of graphs with faulty elements.</abstract>

The product graph Gm *Gp of two given graphs Gm and Gp, defined by J.C. Bermond et al.[J Combin Theory, Series B 36(1984) 32-48] in the context of the so-called (Δ,D)-problem, is one interesting model in the design of large reliable networks. This work deals with sufficient conditions that guarantee these product graphs to be hamiltonian-connected. Moreover, we state product graphs for which provide panconnectivity of interconnection networks modeled by a product of graphs with faulty elements.

Hamilton-connectivity of Interconnection Networks Modeled by a Product of Graphs

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Hamilton-connectivity of Interconnection Networks Modeled by a Product of Graphs"}

The product graph Gm *Gp of two given graphs Gm and Gp, defined by J.C. Bermond et al.[J Combin Theory, Series B 36(1984) 32-48] in the context of the...

Hamilton-connectivity of Interconnection Networks Modeled by a Product of Graphs

Published Online: Dec 07, 2018

Page range: 419 - 426

Received: Mar 15, 2018

Accepted: Jul 30, 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00032

Keywords
panconnected, fault-hamiltonicity, fault tolerance, interconnection networks

© 2018 Donglin Liu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Hamilton-connectivity of Interconnection Networks Modeled by a Product of Graphs

Published Online: Dec 07, 2018

Page range: 419 - 426

Received: Mar 15, 2018

Accepted: Jul 30, 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00032

Keywordspanconnected, fault-hamiltonicity, fault tolerance, interconnection networks

© 2018 Donglin Liu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
panconnected, fault-hamiltonicity, fault tolerance, interconnection networks