{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:02:25Z","timestamp":1760230945388,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,21]],"date-time":"2022-08-21T00:00:00Z","timestamp":1661040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The symmetry of an interconnection network plays a key role in defining the functioning of a system involving multiprocessors where thousands of processor-memory pairs known as processing nodes are connected. Addressing the processing nodes helps to create efficient routing and broadcasting algorithms for the multiprocessor interconnection networks. Oxide interconnection networks are extracted from the silicate networks having applications in multiprocessor systems due to their symmetry, smaller diameter, connectivity and simplicity of structure, and a constant number of links per node with the increasing size of the network can avoid overloading of nodes. The fault tolerant partition basis assigns unique addresses to each processing node in terms of distances (hops) from the other subnets in the network which work in the presence of faults. In this manuscript, the partition and fault tolerant partition resolvability of oxide interconnection networks have been studied which include single oxide chain networks (SOXCN), rhombus oxide networks (RHOXN) and regular triangulene oxide networks (RTOXN). Further, an application of fault tolerant partition basis in case of region-based routing in the networks is included.<\/jats:p>","DOI":"10.3390\/sym14081740","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T01:56:40Z","timestamp":1661133400000},"page":"1740","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fault Tolerant Addressing Scheme for Oxide Interconnection Networks"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0568-1592","authenticated-orcid":false,"given":"Asim","family":"Nadeem","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Sciences, University of Management and Technology, C-II M. A Johar Town, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1097-3450","authenticated-orcid":false,"given":"Agha","family":"Kashif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences, University of Management and Technology, C-II M. A Johar Town, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sohail","family":"Zafar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences, University of Management and Technology, C-II M. A Johar Town, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4099-5025","authenticated-orcid":false,"given":"Amer","family":"Aljaedi","sequence":"additional","affiliation":[{"name":"College of Computing and Information Technology, University of Tabuk, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oluwatobi","family":"Akanbi","sequence":"additional","affiliation":[{"name":"Computer Science Department, University of Colorado, Colorado Springs, CO 80918, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/12.46277","article-title":"Addressing, routing, and broadcasting in hexagonal mesh multiprocessors","volume":"39","author":"Chen","year":"1990","journal-title":"IEEE Trans Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1109\/71.329665","article-title":"Fault tolerant routing in mesh architectures","volume":"5","author":"Olson","year":"1994","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1016\/j.jpdc.2003.07.001","article-title":"Higher dimensional hexagonal networks","volume":"63","author":"Solano","year":"2003","journal-title":"J. Parallel Distrib. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mejia, A., Flich, J., Reinemo, S.A., and Skeie, T. (2006, January 25\u201329). Segment-based routing: An efficient fault-tolerant routing algorithm for meshes and tori. Proceedings of the 20th IEEE International Parallel & Distributed Processing Symposium, Rhodes, Greece.","DOI":"10.1109\/IPDPS.2006.1639341"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1109\/TVLSI.2008.2012010","article-title":"Region-Based Routing: A mechanism to support efficient routing algorithms in NoCs","volume":"17","author":"Mejia","year":"2009","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"71521","DOI":"10.1109\/ACCESS.2022.3188319","article-title":"Fault-tolerant partition resolvability in mesh related networks and applications","volume":"10","author":"Azhar","year":"2022","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bossard, A., and Kaneko, K. (2020). Cluster-fault tolerant routing in a torus. Sensors, 20.","DOI":"10.3390\/s20113286"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Choudhary, A., Kumar, S., Gupta, S., Gong, M., and Mahanti, A. (2021). FEHCA: A Fault-tolerant energy-efficient hierarchical clustering algorithm for wireless sensor networks. Energies, 14.","DOI":"10.3390\/en14133935"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1109\/71.282556","article-title":"Interleaved all-to-all reliable broadcast on meshes and hypercubes","volume":"5","author":"Lee","year":"1994","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Nain, Z., Ali, R., Anjum, S., Afzal, M.K., and Kim, S.W. (2020). A network adaptive fault-tolerant routing algorithm for demanding latency and throughput applications of network-on-a-chip designs. Electronics, 9.","DOI":"10.3390\/electronics9071076"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhou, S., Bai, J., and Wu, F. (2021). Decentralized fault detection and fault-tolerant control for nonlinear Interconnected Systems. Processes, 9.","DOI":"10.3390\/pr9040591"},{"key":"ref_12","first-page":"6540754","article-title":"Molecular descriptors of nanotube, oxide, silicate, and triangulene networks","volume":"2017","author":"Gao","year":"2017","journal-title":"Hindawi J. Chem."},{"key":"ref_13","first-page":"730","article-title":"Topological indices of rhombus type silicate and oxide networks","volume":"95","author":"Javaid","year":"2016","journal-title":"Can. J. Chem."},{"key":"ref_14","first-page":"1778","article-title":"On the metric dimension of silicate stars","volume":"10","author":"Raj","year":"2015","journal-title":"JES"},{"key":"ref_15","first-page":"2278","article-title":"Fault-Tolerant Resolvability of Oxide Interconnections","volume":"8","author":"Somasundari","year":"2019","journal-title":"Int. J. Innov. Technol. Explor. Eng."},{"key":"ref_16","unstructured":"Slater, P.J. (1975, January 17\u201320). Leaves of Trees. Proceedings of the 6th Southeastern Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, Boca Raton, FL, USA. Congressus Numerantium."},{"key":"ref_17","first-page":"191","article-title":"On the metric dimension of a graph","volume":"2","author":"Harary","year":"1976","journal-title":"Theory Comput. Syst. Ars Comb."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0166-218X(95)00106-2","article-title":"Landmarks in Graphs","volume":"70","author":"Khuller","year":"1996","journal-title":"Discrete Appl. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0166-218X(00)00198-0","article-title":"Resolvability in graphs and the metric dimension of a graph","volume":"105","author":"Chartrand","year":"2000","journal-title":"Discrete Appl. Math."},{"key":"ref_20","unstructured":"Garey, M.R., and Johnson, D.S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/PL00000127","article-title":"The partition dimension of a graph","volume":"59","author":"Chartrand","year":"2000","journal-title":"Aequ. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.procs.2015.12.076","article-title":"The partition dimension of some families of trees","volume":"74","author":"Fredlina","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"012012","DOI":"10.1088\/1742-6596\/855\/1\/012012","article-title":"On the partition dimension of a lollipop graph and a generalized Jahangir graph","volume":"855","author":"Dewi","year":"2017","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"343","DOI":"10.3934\/Math.2018.3.343","article-title":"On the partition dimension of fullerene graphs","volume":"3","author":"Mehreen","year":"2018","journal-title":"AIMS Math."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"012070","DOI":"10.1088\/1742-6596\/974\/1\/012070","article-title":"The partition dimension of cycle books graph","volume":"974","author":"Santoso","year":"2018","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_26","first-page":"381","article-title":"On the partition dimension of unicyclic graphs, Bulletin Math\u00e9matique De La Soci\u00e9t\u00e9 Des Sciences Math\u00e9matiques De Roumanie","volume":"57","author":"Fernau","year":"2014","journal-title":"Nouvelle S\u00e9rie"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1166\/jctn.2015.3717","article-title":"Computation of metric dimension and partition dimension of nanotubes","volume":"12","author":"Siddiqui","year":"2015","journal-title":"J. Comput. Theor. Nanosci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.tcs.2018.09.022","article-title":"On the k-partition dimension of graphs","volume":"806","year":"2020","journal-title":"Theor. Comput. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"7282245","DOI":"10.1155\/2021\/7282245","article-title":"On fault-tolerant partition dimension of homogeneous caterpillar graphs","volume":"2021","author":"Azhar","year":"2021","journal-title":"Math. Probl. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7237168","DOI":"10.1155\/2021\/7237168","article-title":"Fault tolerant partition resolvability of cyclic networks","volume":"2021","author":"Azhar","year":"2021","journal-title":"J. Math."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.3233\/JIFS-201390","article-title":"On fault-tolerent partition dimension of graphs","volume":"40","author":"Azhar","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_32","first-page":"3429091","article-title":"On the fault tolerant partition resolvability of toeplitz networks","volume":"2022","author":"Nadeem","year":"2022","journal-title":"Math. Probl. Eng."},{"key":"ref_33","first-page":"3238293","article-title":"Fault tolerant partition resolvability in convex polytoes","volume":"2022","author":"Nadeem","year":"2022","journal-title":"Math. Probl. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"9493","DOI":"10.3233\/JIFS-201982","article-title":"On 2-partition dimension of the circulant graphs","volume":"40","author":"Nadeem","year":"2021","journal-title":"J. Intell. Fuzzy Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1740\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:13:03Z","timestamp":1760141583000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1740"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,21]]},"references-count":34,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["sym14081740"],"URL":"https:\/\/doi.org\/10.3390\/sym14081740","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,8,21]]}}}