Original question and givens
The finite simple undirected graph has V={9, 10, 11, 12} and E={{9, 10}, {9, 11}, {10, 11}}. There are no loops or multiple edges, and repeated representations of the same unordered edge count once. The vertex v=11 belongs to V. Find deg(v).
G001 — The finite simple undirected graph has V={9, 10, 11, 12} and E={{9, 10}, {9, 11}, {10, 11}}. There are no loops or multiple edges, and repeated representations of the same unordered edge count once. The vertex v=11 belongs to V. Find deg(v).
Step-by-step derivation
S001 · implies
Before
source roles = [qf-simple-graph-degree, [E, V, operation, v]]
After
derived = [degree, no-invented-domain]
Conditions: none
Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract.
Step identifiers and dependencies
Rule: R69_SOURCE_specific_keys_operation_domain_AND_binary_contract · Uses: G001
S002 · implies
Before
source roles = [LDL graph vertices ORIGINAL, 100, [9, 10, 11, 12]]
After
derived = [[9, 10, 11, 12]]
Conditions: none
Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits.
Step identifiers and dependencies
Rule: Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort · Uses: G001, S001
S003 · implies
Before
source roles = [LDL raw edges ORIGINAL, 0, [9, 10]]
After
derived = [[9, 10]]
Conditions: none
BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.
Step identifiers and dependencies
Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S002
S004 · implies
Before
source roles = [LDL raw edges ORIGINAL, 1, [9, 11]]
After
derived = [[9, 11]]
Conditions: none
BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.
Step identifiers and dependencies
Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S003
S005 · implies
Before
source roles = [LDL raw edges ORIGINAL, 2, [10, 11]]
After
derived = [[10, 11]]
Conditions: none
BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.
Step identifiers and dependencies
Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S004
S006 · implies
Before
source roles = [[9, 10, 11, 12], [[9, 10], [9, 11], [10, 11]], No]
After
derived = [[[9, 10], [9, 11], [10, 11]], [[9, [10, 11]], [10, [9, 11]], [11, [9, 10]], [12, []]]]
Conditions: none
Type the WHOLE raw edge list,then normalize undirected endpoints/deduplicate;reversed duplicates are allowed.INPUT edges have no loops/outside endpoints,while isolated vertices stay in V.TREE raw E does NOT acquire LDL’s200-entry limit.
Step identifiers and dependencies
Rule: Graph_WHOLE_simple_undirected_edges_normalized_NO_loops_or_outside · Uses: G001, S005
S007 · implies
Before
source roles = [11, [9, 10, 11, 12]]
After
derived = [[9, 10], 2]
Conditions: none
A degree/neighbor QUERY first requires v∈V.Find distinct neighbors through ALL edges,not sketch crossings or raw duplicate rows.
Step identifiers and dependencies
Rule: Graph_QUERY_vertex_must_belong_V_complete_distinct_neighbors · Uses: G001, S006