kvertex

Kvertex, often written as k-vertex or kvertex, is a term encountered in graph theory and related areas to denote a vertex that carries a parameter k. The specific meaning of k can vary by context, but the designation is commonly used to reference a vertex whose local property is described by k, such as its degree in the graph.

In many texts, a k-vertex is simply a vertex of degree k, i.e., a vertex incident to exactly k edges. This use is informal; the standard term for such a vertex is a degree-k vertex. The label k may also denote other quantities depending on the discussion, such as a threshold, a neighborhood size, or a step in an iterative algorithm.

Examples and usage: In a graph with vertices A, B, C, D where A has degree 3, A is a 3-vertex. In a simple cycle of length five, each vertex is a 2-vertex. In problem settings, algorithms may target sets of k-vertices for tasks such as sampling, pruning, or identifying nodes with specific connectivity.

Relation to related concepts: The idea is related to degree sequences, k-core decomposition, and k-regular graphs, but k-vertex itself is not a distinct mathematical object beyond describing the local property of a vertex. When encountered, readers should consult the defining context to determine what k represents.