query: How many graphs have $n$ vertices and $m$ edges?
positive_passages.docid: 59247
positive_passages.text: How many connected graphs over V vertices and E edges?
negative_passages.docid: 75101
negative_passages.text: Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
negative_passages.docid: 91229
negative_passages.text: Complexity of counting the number of triangles of a graph
negative_passages.docid: 154564
negative_passages.text: Prove that the sum of minimum edge cover and maximum matching is the vertex count
negative_passages.docid: 48692
negative_passages.text: A problem about the graph theory
negative_passages.docid: 147282
negative_passages.text: Prove that in every graph with at least two vertices, there are at least two vertices which have the same degree?
negative_passages.docid: 85541
negative_passages.text: What is the maximum length of a circuit in the complete graph on n vertices.
negative_passages.docid: 127277
negative_passages.text: Graph Theory: Tree has at least 2 vertices of degree 1
negative_passages.docid: 93304
negative_passages.text: How to prove Graph with $n$ vertices has Edge Chromatic Number no more than $n/2$ edges
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: 129002
negative_passages.text: Number of triangles formed by $m$ lines
negative_passages.docid: 99781
negative_passages.text: Proof that any simple connected graph has at least 2 non-cut vertices.
negative_passages.docid: 142103
negative_passages.text: find all self-complementary graphs on five vertices
negative_passages.docid: 65622
negative_passages.text: Maximum edges in a square free graph
negative_passages.docid: 149538
negative_passages.text: graph theory - clique graph
negative_passages.docid: 100289
negative_passages.text: Question about self-complementary graphs
negative_passages.docid: 13226
negative_passages.text: If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree?