An Almost Deterministic Algorithm for Finding All Possible Metric Bases of Certain Hamming Graphs
摘要
Metric dimension of a graph provides an efficient way to identify and distinguish genomic sequences by using a small set of reference points. A metric basis for a graph \(G\) (V,E) is a resolving set \(W \subseteq V\) where for any two vertices \(u\) and \(v\) of \(V\backslash W\) , a vertex \(w \in W\) exists for which \(d\left({u,w} \right) \ne d\left({v,w} \right)\) . The cardinality of minimum resolving set is called the metric dimension of a graph G. Genetic sequencing is becoming more widely available and affordable, offering essential genomic information that is frequently expressed as \(k\) -mers. Hamming graphs offer an effective approach for analyzing and comparing biological sequences. In order to better understand and predict genetic features, disease susceptibility, and evolutionary links, the metric dimension of Hamming graphs is essential. In this research, we determine the metric dimension of certain Hamming graphs and extract all possible metric bases using BIGS algorithm which is an almost deterministic algorithm.