Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Articles Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Some New Results on ?(k) -Coloring of Graphs Subject The topic of the resource bad edges; Improper coloring; near proper coloring; ?(k) -coloring Description An account of the resource Let ? be the minimum number of distinct resources or equipment such as channels, transmitters, antennas and surveillance equipment required for a system's stability. These resources are placed on a system. The system is stable only if the resources of the same type are placed far away from each other or, in other words, they are not adjacent to each other. Let these distinct resources represent different colors assigned on the vertices of a graph G. Suppose the available resources, denoted by k, are less than ?. In that case, placing k resources on the vertices of G will make at least one equipment of the same type adjacent to each other, which thereby make the system unstable. In ?(k)-coloring, the adjacency between the resources of a single resource type is tolerated. The remaining resources are placed on the vertices so that no two resources of the same type are adjacent to each other. In this paper, we discuss some general results on the ?(k)-coloring and the number of bad edges obtained from the same for a graph G. Also, we determine the minimum number of bad edges obtained from ?(k)-coloring of few derived graph of graphs. The number of bad edges which result from a ?(k)-coloring of G is denoted by bk(G). 2023 World Scientific Publishing Company. Creator An entity primarily responsible for making the resource Ellumkalayil M.T.; Samuel L.C.; Naduvath S. Source A related resource from which the described resource is derived Journal of Interconnection Networks, Vol-23, No. 3 Publisher An entity responsible for making the resource available World Scientific Date A point or period of time associated with an event in the lifecycle of the resource 2023-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1142/S0219265922500104" target="_blank" rel="noreferrer noopener">https://doi.org/10.1142/S0219265922500104</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85148725961&amp;doi=10.1142%2FS0219265922500104&amp;partnerID=40&amp;md5=a075f1bbb1110a80bf7f7f78500da013" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85148725961&amp;doi=10.1142%2fS0219265922500104&amp;partnerID=40&amp;md5=a075f1bbb1110a80bf7f7f78500da013</a> Rights Information about rights held in and over the resource Restricted Access Relation A related resource ISSN: 2192659 Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Ellumkalayil M.T., School of Sciences, Christ University, Delhi NCR, 201003, India; Samuel L.C., Department of Computer Science, Dasve Lavasa, Mulshi, Pune, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India