- Tytuł:
- On Order Prime Divisor Graphs of Finite Groups
- Autorzy:
-
Sen, Mridul K.
Maity, Sunil K.
Das, Sumanta - Tematy:
-
group
dihedral group
complete graph
Eulerian graph
regular graph
planar graph
order prime divisor graph - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/55795862.pdf Link otwiera się w nowym oknie
- Opis:
- The order prime divisor graph \(\mathscr{PD}(G)\) of a finite group $G$ is a simple graph whose vertex set is $G$ and two vertices $a, b ∈ G$ are adjacent if and only if either $ab = e$ or $o(ab)$ is some prime number, where $e$ is the identity element of the group $G$ and $o(x)$ denotes the order of an element $x ∈ G$. In this paper, we establish the necessary and sufficient condition for the completeness of order prime divisor graph \(\mathscr{PD}(G)\) of a group $G$. Concentrating on the graph \(\mathscr{PD}(D_n)\), we investigate several properties like degrees, girth, regularity, Eulerianity, Hamiltonicity, planarity etc. We characterize some graph theoretic properties of \(\mathscr{PD}(ℤ_n), \mathscr{PD}(S_n), \mathscr{PD}(A_n)\).
- Dostawca treści:
- Biblioteka Nauki
Artykuł