Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Heawood graph | Statement: [PSL(2,7), hasCayleyGraphRelatedTo, Heawood graph]

Target entity: Heawood graph
Context triple: [PSL(2,7), hasCayleyGraphRelatedTo, Heawood graph]

• A. Szekeres snark
  The Szekeres snark is a famous cubic graph in graph theory that serves as a counterexample in edge-coloring problems and helped advance the study of snark graphs.
• B. Szekeres configuration
  The Szekeres configuration is a notable geometric arrangement in projective geometry consisting of points and lines with specific incidence properties, studied for its combinatorial and symmetry characteristics.
• C. Graham–Pollak theorem
  The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
• D. Conway's 99-graph problem
  Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
• E. Fano plane chosen
  The Fano plane is the smallest finite projective plane, consisting of seven points and seven lines with rich symmetrical and combinatorial properties.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasCayleyGraphRelatedTo
Context triple: [PSL(2,7), hasCayleyGraphRelatedTo, Heawood graph]

• A. associatedCayleyGraph chosen
  Indicates that there is a Cayley graph constructed from, or corresponding to, the given algebraic structure or group.
• B. hasHomomorphism
  Indicates that there exists a structure-preserving map (homomorphism) from one mathematical structure to another.
• C. hasConjugacyClasses
  Indicates that a group is associated with specific conjugacy classes, each consisting of elements that are mutually conjugate within the group.
• D. isConwayGroup
  Indicates that the subject is one of the Conway groups, a specific family of sporadic simple groups associated with the Leech lattice in group theory.
• E. hasAutomorphism
  Indicates that there exists a structure-preserving bijection from an entity to itself that maintains all relevant relations and operations.
• F. None of above.