Evenlevel

Evenlevel is a term used informally in mathematics and computer science to refer to a parity-related property tied to a level, depth, or layer within a structured object. There is no single, canonical definition, and meanings vary by field and author.

In rooted graphs or trees, evenlevel often means the set of nodes whose distance from a designated root is even (levels 0, 2, 4, ...). This partition is used in BFS-based analyses and parity arguments, such as counting edges between even and odd levels or designing algorithms that exploit level parity.

Some works refer to evenlevel labeling where vertices are assigned labels according to their level parity, with the aim of achieving certain invariants or balance properties. In practice, this can help optimize traversals or storage layouts by segregating even- and odd-level nodes.

In topology, level-set, or Morse-theoretic contexts, evenlevel can describe sublevel sets or symmetry conditions when a function is constrained to exhibit even-level parity, or when considering filtrations that progress in even-valued steps.

See also: Level, Level graph, Parity, BFS traversal, Level set. Because the term lacks a universal definition, readers should consult field-specific sources for precise meaning.