Between the enhanced power graph and the commuting graph
نویسندگان
چکیده
The purpose of this note is to define a graph whose vertex set finite group G $G$ , edge contained in that the commuting and contains enhanced power . We call deep Two elements are joined if only their inverse images every central extension commute. give conditions for be equal either graph, show automorphisms act as graph.
منابع مشابه
Some Graph Polynomials of the Power Graph and its Supergraphs
In this paper, exact formulas for the dependence, independence, vertex cover and clique polynomials of the power graph and its supergraphs for certain finite groups are presented.
متن کاملon the relation between the non-commuting graph and the prime graph
given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...
متن کاملOn the diameter of the commuting graph of the full matrix ring over the real numbers
In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{M}_n(mathbb{R})$ is equal to $4$ if either $n=3$ or $ngeq5$. But the case $n=4$ remained open, since the diameter could be $4$ or $5$. In this work we close the problem showing that also in this case the diameter is $4$.
متن کاملOn the Relation between the Non-commuting Graph and the Prime Graph
Given a non-abelian finite group G, let π(G) denote the set of prime divisors of the order of G and denote by Z(G) the center of G. The prime graph of G is the graph with vertex set π(G) where two distinct primes p and q are joined by an edge if and only if G contains an element of order pq and the non-commuting graph of G is the graph with the vertex set G−Z(G) where two non-central elements x...
متن کاملOn the Structure of the Power Graph and the Enhanced Power Graph of a Group
Let G be a group. The power graph of G is a graph with the vertex set G, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique/chromatic number. Furthermore, it is proved that for every grou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2022
ISSN: ['0364-9024', '1097-0118']
DOI: https://doi.org/10.1002/jgt.22871