Let G be a graph and k a natural number. A k-coloring of G is a map c that maps the vertices of G into the set {1, 2, ..., k} (whose elements are called colors) such that no two adjacent vertices are ...

Key Features: Graph Representation: The graph is represented using an adjacency matrix, where 1 denotes an edge between two vertices and 0 denotes no edge. Color Assignment: The program uses a greedy ...

For example, an endpoint of a path is a zero forcing set for the path. In a cycle, any set of two adjacent vertices is a zero forcing set. Corollary 2.2 [1,5] Let be a graph and let be a zero forcing ...

For a simple undirected connected graph, if there exists a one-to-one mapping of the set of edges, which is labeled and the same for all adjacent vertices of the same degree in the graph, then it is ...