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- Title
Research on the Algorithm of Adjacent Vertex Reducible Total Labeling for Graphs.
- Authors
Jiang Wang; Jingwen Li; Xin Gao; Cong Huang
- Abstract
For an undirected connected graph G(V, E), if there exists a unique mapping f:V(G) ∪ E(G) &#8594 {1,2, ⋯, |V| + E|}, such that for any edge uv ∈ E(G) and d(u) = d(v), it holds that S(u) = S(v), where S(u) = f(u) + ∑uz∈E(G)f(uz), and d(u) represents the degree of vertex u, then f is termed as an Adjacent Vertex Reducible Total Labeling (AVRTL) of G. Building upon existing research on total labeling algorithms, a heuristic search algorithm is devised by combining principles from genetic algorithm and particle swarm optimization. By studying the labeling patterns within finite-point graphs and extending them to describe the labeling patterns of infinite-point analogous graphs, it is discovered that some composite graphs of AVRTL are derived from several special subgraphs that are also AVRTL through a graph operation. Several theorems summarizing the labeling characteristics of these composite graphs are formulated and proven, along with defining the graph operation. Finally, a conjecture is proposed: if subgraphs G1 and G2 are AVRTL graphs, then their composite graph G1 ↑anb G2 is also an AVRTL graph, where ↑ab denotes the graph operation.
- Subjects
PARTICLE swarm optimization; GRAPH labelings; HEURISTIC algorithms; ALGORITHMS; HEURISTIC; SEARCH algorithms
- Publication
IAENG International Journal of Applied Mathematics, 2024, Vol 54, Issue 7, p1435
- ISSN
1992-9978
- Publication type
Article