Research on Magic Edge Colouring Algorithm for Point Classification Based on Aggregation Coefficients

Suppose G(V, E) is a simple connected graph, if there exists a positive integer k(1 ≤
$k$
≤ | E|) and a mapping f: E (G) → {1, 2, · · ·, k}, such that for any two points u, v E C
i
(G), V(G) = U
^j
i Ci(G), i = 1,2,···, j, S(u) - S(v) = θ S(u) = Σ uwεE
^f
(uw) and uwεE(G). All vertices in the graph are divided into
$j$
classes according to equal aggregation coefficients, C
i
(G) denotes a vertex of class
$i$
, then
$f$
is said to be an Aggregation Vertex Classification Magic Edge Coloring(A Vcmec)based on the aggregation coefficient of
$G$
and, Xavcmec (G) = max {k|
$k$
- A VCMECK of G}. is called the magic edge colour number for point classification based on aggregation coefficients. In this paper, based on the concept of colouring of existing graphs, combined with the feature parameters of complex networks, the concept of magic edge colouring for point classification based on aggregation coefficients is proposed. An aggregation coefficient based magic edge colouring algorithm for point classification is designed. After experimental analysis, the staining theorems of several road graphs, circle graphs and friendship graphs are summarized and proofs are given. Besides, the maximum staining numbers of road traffic networks under different constraints are given to prove the correctness of the algorithm.