Check all that apply - Please note that only the first page is available if you have not selected a reading option after clicking "Read Article". Thank you for everything! 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 1& 1& 0& 0& 1\\ (a) Construct a graph of order 5 with degrees of vertices being 4,4,3,2,2. Most efficient and feasible non-rocket spacelaunch methods moving into the future? 0& 1& 0& 1& 0& 1& 0& 1& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ How to label resources belonging to users in a two-sided marketplace? Show that G is a tree if and only if the addition of any edge to G produces exactly 1 new cycle. Definition â A graph (denoted as G = (V, E)) consists of a non-empty set of vertices or nodes V and a set of edges E. Use MathJax to format equations. x_{i,j} + \sum_{k \in N \setminus \{i,j\}} y_{i,j,k} &\ge 1 &&\text{for $(i,j)\in P$} \tag2\\ 1& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 1& 0& 1& 0& 0& 1& 0& 0& 0& 0\\ Let G be a graph on n vertices, G 6= Kn. 0& 0& 0& 0& 0& 0& 0& 1& 0& 1& 0& 0& 1& 1& 1& 0& 0& 0& 0& 0& 0& 0\\ It is the unique (up to graph isomorphism) self-complementary graphon a set of 5 vertices Note that 5 is the only size for which the Paley graph coincides with the cycle graph. I am not familiar with such nomenclature. 0& 0& 1& 0& 1& 0& 0& 0& 0& 1& 1& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ :) Thank you! Do not surround your terms in double-quotes ("") in this field. Most of the constructed graphs have more than 1000 vertices, and the number of vertices goes up to 28431. I think I understand the construction method you have mentioned, however I cannot see how the diameter should be 2. \begin{align} Following are some regular graphs. Proof: In a complete graph of N vertices, each vertex is connected to all (N-1) remaining vertices. 1& 0& 1& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 1& 0\\ Another strongly regular graph with the same parameters is constructed on the codewords of the dual code. Thanks for helping us catch any problems with articles on DeepDyve. Thank you, this one is perfect. 0& 1& 1& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 0& 0& 0& 0& 0& 1& 0& 0\\ We are working on a paper in which we needed such a graph, but I have sent you a detailed e-mail in connection with this, I hope that you will see it. that matters to you. 0& 0& 0& 1& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 1& 0& 0\\ EXERCISE: Draw two 3-regular graphs with six vertices. The one on 24 vertices can be constructed with the help of twisted or star product ($K_3*X_8$), however as I see such twisted product cannot work on 22 vertices, and there are about $10^{19}$ connected 5-regular graphs on 22 vertices, so generating all of them and selecting those with diameter 2 is hopeless for me. Unlimited access to over18 million full-text articles. It is the Paley graph corresponding to the field of 5 elements 3. 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 1& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1& 0\\ Thank you for the answers! MathJax reference. It has 5 10-cocliques and 10+450=460 5-cliques. 0& 0& 0& 1& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 1& 0& 0\\ \end{matrix}. Asking for help, clarification, or responding to other answers. Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. Why the sum of two absolutely-continuous random variables isn't necessarily absolutely continuous? You are asking for regular graphs with 24 edges. Why should we use the fundamental definition of derivative while checking differentiability? In general, the Paley graph can be expressed as an edge-disjoint union of cycle graphs. Let $N=\{1,\dots,22\}$ be the nodes, and let \$P=\{i\in N, j\in N: i