ArticlePloS one2025
A novel approach to explore common prime divisor graphs and their degree based topological descriptor.
Article in PloS one, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
For the construction of a common prime divisor graph, we consider an integer [Formula: see text] with its prime factorization, where [Formula: see text] are distinct primes and [Formula: see text] are fixed positive integers. Every divisor of the integer [Formula: see text] has the form [Formula: see text], with [Formula: see text]. There are [Formula: see text] distinct divisors of integer [Formula: see text]. Let [Formula: see text] be the collection of all positive divisors of [Formula: see text] other than integer 1. Then we can define a simple graph on the set of divisors [Formula: see text] of [Formula: see text], called a common prime divisor graph [Formula: see text] with [Formula: see text] as the vertex set, and we insert an edge between two distinct divisors x and y of [Formula: see text] if the [Formula: see text]. In this article, we will introduce and discuss some basic properties of common prime divisor graphs and we will compute some indices of symmetries associated with a class of such graphs. This study will open a new domain of graphs to investigate their invariant and to explore such indices on the different classes of common prime divisor graphs.
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