Mathbox for Alexander van der Vekens < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-uvtxa Structured version   Visualization version   Unicode version

Definition df-uvtxa 39567
 Description: Define the class of all universal vertices (in graphs). A vertex is called universal if it is adjacent, i.e. connected by an edge, to all other vertices (of the graph) resp. all other vertices are its neighbors. (Contributed by Alexander van der Vekens, 12-Oct-2017.) (Revised by AV, 24-Oct-2020.)
Assertion
Ref Expression
df-uvtxa UnivVtx Vtx Vtx NeighbVtx
Distinct variable group:   ,,

Detailed syntax breakdown of Definition df-uvtxa
StepHypRef Expression
1 cuvtxa 39562 . 2 UnivVtx
2 vg . . 3
3 cvv 3031 . . 3
4 vn . . . . . . 7
54cv 1451 . . . . . 6
62cv 1451 . . . . . . 7
7 vv . . . . . . . 8
87cv 1451 . . . . . . 7
9 cnbgr 39561 . . . . . . 7 NeighbVtx
106, 8, 9co 6308 . . . . . 6 NeighbVtx
115, 10wcel 1904 . . . . 5 NeighbVtx
12 cvtx 39251 . . . . . . 7 Vtx
136, 12cfv 5589 . . . . . 6 Vtx
148csn 3959 . . . . . 6
1513, 14cdif 3387 . . . . 5 Vtx
1611, 4, 15wral 2756 . . . 4 Vtx NeighbVtx
1716, 7, 13crab 2760 . . 3 Vtx Vtx NeighbVtx
182, 3, 17cmpt 4454 . 2 Vtx Vtx NeighbVtx
191, 18wceq 1452 1 UnivVtx Vtx Vtx NeighbVtx
 Colors of variables: wff setvar class This definition is referenced by:  uvtxaval  39623
 Copyright terms: Public domain W3C validator