query: Self-complementary graph with 4k+1 vertices, which is 2k-regular
positive_passages.docid: 26251
positive_passages.text: Prove self-complementarity of regular graph with given order.
negative_passages.docid: 19219
negative_passages.text: On the invertibility of the adjacency matrix of a graph
negative_passages.docid: 128034
negative_passages.text: Problem on Extremal Graphs: three independent paths
negative_passages.docid: 124666
negative_passages.text: Hamiltonian and non-Hamiltonian connected graph using the same degree sequence
negative_passages.docid: 102539
negative_passages.text: Min. number of vertices in graph as function of $\kappa(G)$ and $\operatorname{diam}(G)$
negative_passages.docid: 83872
negative_passages.text: Isomorphisms for graphs with loops and multiple edges
negative_passages.docid: 44563
negative_passages.text: Weakly Connected Graphs
negative_passages.docid: 108417
negative_passages.text: Cycles of length k in a complete simple graph with n vertices
negative_passages.docid: 100466
negative_passages.text: The number of labelled graphs with all vertices of even degree
negative_passages.docid: 90559
negative_passages.text: Partitioning of a graph
negative_passages.docid: 142861
negative_passages.text: Multipartite graphs which are not planar
negative_passages.docid: 53924
negative_passages.text: What is the smallest $n$ for which loopless graphs contain non-isomorphic $n$-vertex graphs with the same degree sequence?
negative_passages.docid: 50886
negative_passages.text: Two disjoint spanning trees, spanning subgraph with all even degrees
negative_passages.docid: 99781
negative_passages.text: Proof that any simple connected graph has at least 2 non-cut vertices.
negative_passages.docid: 39753
negative_passages.text: Proving that in a simple graph with $n$ vertices, two vertices have the same degree
negative_passages.docid: 49879
negative_passages.text: A bipartite graph with a perfect matching has a vertex with each edge contained in a perfect matching
negative_passages.docid: 19413
negative_passages.text: Degree sequence multigraph without loop