David G. Costanzo

activity

20202026

most citedThe Cyclic Graph of a Z-group

12 citations · 20 across the 6 of their papers we have counts for

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7 papers · 1 filter

math.GR2026

On the local Frattini subgroup of a finite group

David G. Costanzo

Let $G$ be a finite group and let $π (G)$ be the set of prime divisors of $∣ G ∣$ . For each $p \in π (G)$ , choose a Sylow $p$ -subgroup $G_{p}$ of $G$ . The subgroup $Ψ(G)= \prod_{p\in π(G)…

math.GR2024

Characterizing finite groups whose enhanced power graphs have universal vertices

David G. Costanzo, Mark L. Lewis, Stefano Schmidt +2

Let $G$ be a finite group and construct a graph $Δ (G)$ by taking $G ∖ {1}$ as the vertex set of $Δ (G)$ and by drawing an edge between two vertices $x$ and $y$ if $\langle x…

math.GR2024

Finite solvable tidy Groups whose orders are divisible by two primes

Nicolas F. Beike, Rachel Carleton, David G. Costanzo +4

In this paper, we investigate finite solvable tidy groups. We classify the tidy ${p, q}$ -groups. Combining this with a previous result, we are able to characterize the finite t…

math.GR2021

The Cyclic Graph of a $2$ -Frobenius Group

David G. Costanzo, Mark L. Lewis

The cyclic graph of a group $G$ is the graph whose vertices are the nonidentity elements of $G$ and whose edges connect distinct elements $x$ and $y$ if and only if the subgroup $\…

math.GR2021

Extending Morgan and Parker's results about commuting graphs

Nicolas F. Beike, Rachel Carleton, David G. Costanzo +4

Morgan and Parker have proved that if $G$ is a group satisfying the condition that $Z (G) = 1$ , then the connected components of the commuting graph of $G$ have diameter at most $10…

math.GR2020★ 12 cited

The Cyclic Graph of a Z-group

David G. Costanzo, Mark L. Lewis, Stefano Schmidt +2

For a group $G$ , we define a graph $Δ (G)$ by letting $G^{#} = G ∖ {1}$ be the set of vertices and by drawing an edge between distinct elements $x, y \in G^{#}$ if and o…

math.GR2020★ 8 cited

The cyclic graph (deleted enhanced power graph) of a direct product

David G. Costanzo, Mark L. Lewis, Stefano Schmidt +2

Let $G$ be a finite group. Define a graph on the set $G^{#} = G ∖ {1}$ by declaring distinct elements $x, y \in G^{#}$ to be adjacent if and only if $\langle x,y\rangle…

On the local Frattini subgroup of a finite group

Characterizing finite groups whose enhanced power graphs have universal vertices

Finite solvable tidy Groups whose orders are divisible by two primes

The Cyclic Graph of a 2-Frobenius Group

Extending Morgan and Parker's results about commuting graphs

The Cyclic Graph of a Z-group

The cyclic graph (deleted enhanced power graph) of a direct product

The Cyclic Graph of a $2$ -Frobenius Group