The intersection power graph associated with a finite group
نویسندگان
چکیده
منابع مشابه
SOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP
Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...
متن کاملa note on the power graph of a finite group
suppose $gamma$ is a graph with $v(gamma) = { 1,2, cdots, p}$and $ mathcal{f} = {gamma_1,cdots, gamma_p} $ is a family ofgraphs such that $n_j = |v(gamma_j)|$, $1 leq j leq p$. define$lambda = gamma[gamma_1,cdots, gamma_p]$ to be a graph withvertex set $ v(lambda)=bigcup_{j=1}^pv(gamma_j)$ and edge set$e(lambda)=big(bigcup_{j=1}^pe(gamma_j)big)cupbig(bigcup_{ijine(gamma)}{uv;uin v(gamma_i),vin ...
متن کاملThe power graph of a finite group
The power graph of a group is the graph whose vertex set is the group, two elements being adjacent if one is a power of the other. We observe that nonisomorphic finite groups may have isomorphic power graphs, but that finite abelian groups with isomorphic power graphs must be isomorphic. We conjecture that two finite groups with isomorphic power graphs have the same number of elements of each o...
متن کاملsubgroup intersection graph of finite abelian groups
let $g$ be a finite group with the identity $e$. the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$, where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$. in th...
متن کاملOn the punctured power graph of a finite group
The punctured power graph P (G) of a finite group G is the graph which has as vertex set the nonidentity elements of G, where two distinct elements are adjacent if one is a power of the other. We show that P (G) has diameter at most 2 if and only if G is nilpotent and every Sylow subgroup of G is either a cyclic group or a generalized quaternion 2-group. Also, we show that if G is a finite 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: Scienceasia
سال: 2021
ISSN: ['1513-1874']
DOI: https://doi.org/10.2306/scienceasia1513-1874.2021.091