1. Adjacent Vertex Reducible Edge Labeling Algorithm for Several Compound Graphs.
- Author
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Liangjing Sun, Jingwen Li, Cong Huang, and Xin Gao
- Subjects
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GRAPH algorithms , *SEARCH algorithms , *HEURISTIC algorithms , *HEURISTIC , *LABELING laws , *RANDOM graphs , *GRAPH labelings - Abstract
Let G(p,q) be a simple graph, where p is the number of vertices and q is the number of edges if there exists a one-to-one mapping f: E(G)→{1,2,...,|E|}, so that for any two vertices uv∈E(G), if d(u)=d(v), then S(u)=S(v), where ... represents the degree of vertex u, f is called the Adjacent Vertex Reducible Edge Labeling (AVREL) of G. Building on the current graph labeling algorithm, a heuristic search algorithm is designed, and this algorithm is used to label random graphs with less than 12 vertices and obtain the result set of adjacent vertex reducible edge labeling. Based on the analysis of the result set and combining it with the known theorem, the adjacent vertex reducible edge labeling law of other compound graphs is obtained, and the related proof is given. [ABSTRACT FROM AUTHOR]
- Published
- 2024