Use the K-Neighborhood Subgraphs to Compute Canonical Labelings of Graphs

This paper puts forward an innovative theory and method to calculate the canonical labelings of graphs that are distinct to Nauty's. It shows the correlation between the canonical labeling of a graph and the canonical labeling of its complement graph. It regularly examines the link between computing the canonical labeling of a graph and the canonical labeling of its open k-neighborhood subgraph. It defines diffusion degree sequences and entire diffusion degree sequence. For each node of a graph G, it designs a characteristic m_NearestNode to improve the precision for calculating canonical labeling. Two theorems established here display how to compute the first nodes of MaxQ(G). Another theorem presents how to determine the second nodes of MaxQ(G). When computing Cmax(G), if MaxQ(G) already holds the first i nodes u1,u2,MIDLINE HORIZONTAL ELLIPSIS,ui, Diffusion and Nearest Node theorems provide skill on how to pick the succeeding node of MaxQ(G). Further, it also establishes two theorems to determine the Cmax(G) of disconnected graphs. Four algorithms implemented here demonstrate how to compute MaxQ(G) of a graph. From the results of the software experiment, the accuracy of our algorithms is preliminarily confirmed. Our method can be employed to mine the frequent subgraph. We also conjecture that if there is a node v is an element of S(G) meeting conditions Cmax(G-v)<= Cmax(G-w) for each w is an element of S(G)perpendicular to w not equal v, then u1=v for MaxQ(G).