Results 1 to 10 of about 96,071 (258)
The rainbow connection number of the enhanced power graph of a finite group
Electronic Journal of Graph Theory and Applications, 2023 Let G be a finite group. The enhanced power graph ΓGe of G is the graph with vertex set G and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this article, we calculate the rainbow connection number of ΓGe.
Luis A. Dupont +2 more
doaj +3 more sources
On the Connectivity of Enhanced Power Graphs of Finite Groups
Graphs and Combinatorics, 2021 This paper deals with the vertex connectivity of enhanced power graph of finite group. We classify all abelian groups G such that vertex connectivity of enhanced power graph of G is 1. We derive an upper bound of vertex connectivity for the enhanced power graph of any general abelian group G.
Sudip Bera
exaly +4 more sources
On spectrum and energies of enhanced power graphs
Mathematics OpenThe enhanced power graph [Formula: see text] of a group G is a simple graph with vertex set G and two distinct vertex are adjacent if and only if they belong to the same cyclic subgroup.
Pankaj Kalita, Prohelika Das
doaj +2 more sources
On the difference of the enhanced power graph and the power graph of a finite group
Journal of Combinatorial Theory - Series AzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Angsuman Das, Peter Cameron
exaly +5 more sources
Certain properties of the enhanced power graph associated with a finite group
Acta Mathematica Hungarica, 2023 The enhanced power graph of a finite group $G$, denoted by $\mathcal{P}_E(G)$, is the simple undirected graph whose vertex set is $G$ and two distinct vertices $x, y$ are adjacent if $x, y \in \langle z \rangle$ for some $z \in G$. In this article, we determine all finite groups such that the minimum degree and the vertex connectivity of $\mathcal{P}_E(
Kumar, J., Ma, X., Parveen, Singh, S.
exaly +4 more sources
Residual-aware health prediction of power transformers via spatiotemporal graph neural networks. [PDF]
PLoS ONEAccurate health state prediction and timely fault detection of power transformers are critical for ensuring the reliability and resilience of modern power systems. This paper proposes a residual-aware spatiotemporal graph neural network (STGNN) framework
Peng Zeng, Gong Chu
doaj +2 more sources
Forbidden subgraphs in enhanced power graphs of finite groups
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: MatematicasThe enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split and threshold.
Samir Zahirovic +2 more
exaly +4 more sources
An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups
Acta Mathematica Hungarica11 pages, Comments are welcome.
Bera, S., Dey, H. K.
exaly +3 more sources
Between the enhanced power graph and the commuting graph
Journal of Graph Theory, 2022 AbstractThe purpose of this note is to define a graph whose vertex set is a finite group , whose edge set is contained in that of the commuting graph of and contains the enhanced power graph of . We call this graph the deep commuting graph of . Two elements of are joined in the deep commuting graph if and only if their inverse images in every central ...
Peter J. Cameron, Bojan Kuzma
openaire +4 more sources
The cyclic graph (deleted enhanced power graph) of a direct product [PDF]
Involve, a Journal of Mathematics, 2021 Let $G$ be a finite group. Define a graph on the set $G^{\#} = G \setminus \{ 1 \}$ by declaring distinct elements $x,y\in G^{\#}$ to be adjacent if and only if $\langle x,y\rangle$ is cyclic. Denote this graph by $Δ(G)$. The graph $Δ(G)$ has appeared in the literature under the names cyclic graph and deleted enhanced power graph.
Costanzo, David G. +4 more
openaire +2 more sources