Adjacent Vertex Reducible Total Coloring Algorithm for Several Joint Graphs

For a simple graph G(V, E), if there exists a positive integer k (1 ≤ k ≤ |E| + |G|) and a mapping f: V(G) U E(G) → {1, 2, …, k} such that the color sets of adjacent vertices with the same degree are identical, then f represents the Adjacent Vertex Reducible Total Coloring(AVRTC) of the graph G. Building upon the existing research on reducible edge coloring and Adjacent Vertices Reducible Edge Labeling, a new algorithm for Adjacent Vertex Reducible Total Coloring is designed based on practical problems. This algorithm conducts research on several joint graphs through iterative optimization. Analyzing the experimental results obtains the adjacent vertex reducible total chromatic number of some joint graphs, summarizes several theorems, and provides proof.