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Birecognition of prime graphs, and minimal prime graphs

Discrete Mathematics, Algorithms and Applications, 2021
Given a graph [Formula: see text], a subset [Formula: see text] of [Formula: see text] is a module of [Formula: see text] if for each [Formula: see text], [Formula: see text] is adjacent to all the elements of [Formula: see text] or to none of them.
Houmem Belkhechine, Cherifa Ben Salha, P. Ille   +2 more
semanticscholar   +5 more sources

Classifying families of character degree graphs of solvable groups [PDF]

International Journal of Group Theory, 2019
‎We investigate prime character degree graphs of solvable groups‎. ‎In particular‎, ‎we consider a family of graphs $Gamma_{k,t}$ constructed by adjoining edges between two complete graphs in a one-to-one fashion‎.
Mark Bissler, Jacob Laubacher
doaj   +4 more sources

Prime ideal graphs of commutative rings

Indonesian Journal of Combinatorics, 2022
Let R be a finite commutative ring with identity and P be a prime ideal of R. The vertex set is R - {0} and two distinct vertices are adjacent if their product in P. This graph is called the prime ideal graph of R and denoted by ΓP.
Haval Mohammed Salih, Asaad A. Jund
doaj   +2 more sources

On k-prime graphs

Open Mathematics
In the context of a simple undirected graph GG, a kk-prime labeling refers to assigning distinct integers from the set {k,k+1,…,∣V(G)∣+k−1}\left\{k,k+1,\ldots ,| V\left(G)| +k-1\right\} to its vertices, such that adjacent vertices in GG are labeled with ...
Abughneim Omar A., Abughazaleh Baha’
doaj   +2 more sources

ON FINITE PRIME DISTANCE GRAPHS

Indian Journal of Pure and Applied Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Parthiban, G. Samdanielthompson, K. S. Kumar   +2 more
semanticscholar   +3 more sources

Effective Conversion of Non-Prime Graphs to Prime Graphs

International Journal of Analysis and Applications
A graph G is considered to have a prime labeling when each of its n vertices is assigned a unique label from the set {1, 2, 3, 4, ..., n}, ensuring that the labels of any two connected vertices are coprime.
Karnam Gurunadhan Tharunraj, P. Ragukumar   +1 more
semanticscholar   +2 more sources

A novel approach to explore common prime divisor graphs and their degree based topological descriptor. [PDF]

PLoS ONE
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
Ali N A Koam, Azeem Haider, Ali Ahmad, Moin Akhtar Ansari   +3 more
doaj   +2 more sources

Some New Odd prime Graphs

Ratio Mathematica, 2023
For a graph G, a bijection f is called an odd prime labeling , if f from V to f1; 3; 5; ::::; 2jV j - 1g for each edge uv in G the greatest common divisor of the labels of end vertices (f(u); f(v)) is one.
Meena S, Gajalakshmiy G
doaj   +2 more sources

‎$‎4‎$‎-Regular prime graphs of nonsolvable groups [PDF]

International Journal of Group Theory, 2020
Let $G$ be a finite group and $\cd(G)$ denote the character degree set for $G$. The prime graph $\DG$ is a simple graph whose vertex set consists of prime divisors of elements in $\cd(G)$, denoted $\rho(G)$.
Donnie Kasyoki, Paul Oleche
doaj   +3 more sources

Prime labeling of graphs constructed from wheel graph

Heliyon
A prime labeling of a simple undirected graph G is to assign unique integer labels from the set {1,2,...,|V(G)|} to each vertex such that any two adjacent vertices in the graph have labels that are relatively prime.
Baha' Abughazaleh, Omar A. Abughneim
doaj   +3 more sources