http://researchonline.federation.edu.au/vital/access/manager/Index ${session.getAttribute("locale")} 5 On large bipartite graphs of diameter 3 http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:4958 Wed 07 Apr 2021 13:44:33 AEST ]]> On graphs of defect at most 2 http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:4236 0, that is, (Δ,D,-)-graphs. The parameter is called the defect. Graphs of defect 1 exist only for Δ=2. When >1, (Δ,D,-)-graphs represent a wide unexplored area. This paper focuses on graphs of defect 2. Building on the approaches developed in Feria-Purón and Pineda-Villavicencio (2010) [11] we obtain several new important results on this family of graphs. First, we prove that the girth of a (Δ,D,-2)-graph with Δ<4 and D<4 is 2D. Second, and most important, we prove the non-existence of (Δ,D,-2)-graphs with even Δ<4 and D<4; this outcome, together with a proof on the non-existence of (4,3,-2)-graphs (also provided in the paper), allows us to complete the catalogue of (4,D,-)-graphs with D<2 and 0≤≤2. Such a catalogue is only the second census of (Δ,D,-2)-graphs known at present, the first being that of (3,D,-)-graphs with D<2 and 0≤≤2 Jørgensen (1992) [14]. Other results of this paper include necessary conditions for the existence of (Δ,D,-2)-graphs with odd Δ<5 and D<4, and the non-existence of (Δ,D,-2)-graphs with odd Δ<5 and D<5 such that Δ≡0,2(modD). Finally, we conjecture that there are no (Δ,D,-2)-graphs with Δ<4 and D<4, and comment on some implications of our results for the upper bounds of N(Δ,D). © 2011 Elsevier B.V. All rights reserved.]]> Wed 07 Apr 2021 13:43:40 AEST ]]> New largest known graphs of diameter 6 http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:3672 Wed 07 Apr 2021 13:34:41 AEST ]]> Complete catalogue of graphs of maximum degree 3 and defect at most 4 http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1939 Wed 07 Apr 2021 13:33:00 AEST ]]> On bipartite graphs of diameter 3 and defect 2 http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1921 Wed 07 Apr 2021 13:32:58 AEST ]]> On bipartite graphs of defect 2 http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1775 Wed 07 Apr 2021 13:32:50 AEST ]]> Context-dependent security enforcement of statistical databases http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1559 Wed 07 Apr 2021 13:32:39 AEST ]]> On large graphs with given degree and diameter http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1490 Wed 07 Apr 2021 13:32:34 AEST ]]> Properties of consecutive edge magic total graphs http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1488 Wed 07 Apr 2021 13:32:34 AEST ]]> New largest graphs of diameter 6. (Extended Abstract) http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:717 Wed 07 Apr 2021 13:31:41 AEST ]]> Sum graph based access structure in a secret sharing scheme http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:605 Wed 07 Apr 2021 13:31:33 AEST ]]> On irregular total labellings http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:62 Wed 07 Apr 2021 13:30:52 AEST ]]> Vertex-magic total labeling of generalized Petersen graphs and convex polytopes http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:597 Thu 05 Jan 2023 16:47:53 AEDT ]]>