Theorems · Theorem · combinatorics
SimpleGraph.sum_degrees_eq_twice_card_edges
∀ {V : Type u} (G : SimpleGraph V) [inst : Fintype V] [inst_1 : DecidableRel G.Adj],
∑ v, G.degree v = 2 * G.edgeFinset.cardThe degree-sum formula. This is also known as the handshaking lemma, which might
more specifically refer to SimpleGraph.even_card_odd_degree_vertices.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardstatement · cited by 2,327
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Sym2statement · cited by 737
- SimpleGraph.neighborSetstatement · cited by 257
- SimpleGraph.edgeFinsetstatement · cited by 116
- SimpleGraph.degreestatement · cited by 112
- SimpleGraph.dart_card_eq_sum_degreesproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.IsMatching.even_cardproof · cited by 5
- SimpleGraph.even_card_odd_degree_verticesproof · cited by 1
- SimpleGraph.IsTree.minDegree_eq_one_of_nontrivialproof · cited by 0
- SimpleGraph.card_edgeFinset_completeEquipartiteGraphproof · cited by 0