A k-regular graph is a type of graph in which every vertex has the same degree, meaning each vertex is connected to exactly k edges. This uniformity ensures that the graph is balanced, making it easier to analyze and understand its properties. In a k-regular graph, the value of k can vary, leading to different structures. For example, a 3-regular graph has vertices connected to three edges, while a 2-regular graph forms a cycle. These graphs are important in various fields, including network theory and computer science, due to their predictable behavior and symmetry.