Onagh, Bibi N. Roughness in \(G\)-graphs. (English) Zbl 1524.05250 Commentat. Math. Univ. Carol. 61, No. 2, 147-154 (2020). Summary: \(G\)-graphs are a type of graphs associated to groups, which were proposed by A. Bretto and A. Faisant [Math. Slovaca 55, No. 1, 1–8 (2005; Zbl 1119.05054)]. In this paper, we first give some theorems regarding \(G\)-graphs. Then we introduce the notion of rough \(G\)-graphs and investigate some important properties of these graphs. MSC: 05C72 Fractional graph theory, fuzzy graph theory 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:coset; \(G\)-graph; rough set; group; normal subgroup; lower approximation; upper approximation Citations:Zbl 1119.05054 × Cite Format Result Cite Review PDF Full Text: DOI Link References: [1] Badaoui M.; Bretto A.; Ellison D.; Mourad B., On constructing expander families of \(G\)-graphs, Ars Math. Contemp. 15 (2018), no. 2, 425-440 · Zbl 1411.05145 · doi:10.26493/1855-3974.1537.97c [2] Bretto A.; Faisant A., Another way for associating a graph to a group, Math. Slovaca 55 (2005), no. 1, 1-8 · Zbl 1119.05054 [3] Bretto A.; Faisant A., Cayley graphs and \(G\)-graphs: some applications, J. Symbolic Comput. 46 (2011), no. 12, 1403-1412 · Zbl 1236.05100 · doi:10.1016/j.jsc.2011.08.016 [4] Bretto A.; Faisant A.; Gillibert L., \(G\)-graphs: a new representation of groups, J. Symbolic Comput. 42 (2007), no. 5, 549-560 · Zbl 1125.05050 · doi:10.1016/j.jsc.2006.08.002 [5] Bretto A.; Gilibert L., \(G\)-graphs for the cage problem: a new upper bound, International Symp. on Symbolic and Algebraic Computation, ISSAC 2007, ACM, New York, 2007, pages 49-53 · Zbl 1190.05082 [6] Bretto A.; Gillibert L., \(G\)-graphs: an efficient tool for constructing symmetric and semisymmetric graphs, Discrete Appl. Math. 156 (2008), no. 14, 2719-2739 · Zbl 1157.05027 · doi:10.1016/j.dam.2007.11.011 [7] Bretto A.; Jaulin C.; Gillibert L.; Laget B., A new property of Hamming graphs and mesh of \(d\)-ary trees, 8th Asian Symposium, ASCM 2007, Singapore, 2007, Lecture Notes in Artificial Intelligence, Subseries Lecture Notes in Computer Science 5081, 2008, pages 139-150 · Zbl 1166.68332 [8] Cayley A., Desiderata and suggestions: No. 2. The theory of groups: graphical representations, Amer. J. Math. 1 (1878), no. 2, 174-176 · JFM 10.0105.02 · doi:10.2307/2369306 [9] Cayley A., On the theory of groups, Amer. J. Math. 11 (1889), no. 2, 139-157 · JFM 20.0140.01 · doi:10.2307/2369415 [10] Cheng W.; Mo Z.-W.; Wang J., Notes on: “The lower and upper approximations in a fuzzy group” and “Rough ideals in semigroups”, Inform. Sci. 177 (2007), no. 22, 5134-5140 · Zbl 1123.20307 · doi:10.1016/j.ins.2006.12.006 [11] Kuroki N.; Wang P. P., The lower and upper approximations in a fuzzy group, Inform. Sci. 90 (1996), no. 1-4, 203-220 · Zbl 0878.20050 · doi:10.1016/0020-0255(95)00282-0 [12] Pawlak Z., Rough sets, Internat. J. Comput. Inform. Sci. 11 (1982), no. 5, 341-356 · Zbl 0501.68053 · doi:10.1007/BF01001956 [13] Shahzamanian M. H.; Shirmohammadi M.; Davvaz B., Roughness in Cayley graphs, Inform. Sci. 180 (2010), no. 17, 3362-3372 · Zbl 1231.05125 · doi:10.1016/j.ins.2010.05.011 [14] West D. B., Introduction to Graph Theory, Prentice Hall, Upper Saddle River, 1996 · Zbl 1121.05304 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.