Intersection graphs of maximal hypercubes
نویسندگان
چکیده
منابع مشابه
On cycles in intersection graphs of rings
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...
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The intersection graph $mathbb{Int}(A)$ of an $S$-act $A$ over a semigroup $S$ is an undirected simple graph whose vertices are non-trivial subacts of $A$, and two distinct vertices are adjacent if and only if they have a non-empty intersection. In this paper, we study some graph-theoretic properties of $mathbb{Int}(A)$ in connection to some algebraic properties of $A$. It is proved that the fi...
متن کاملon cycles in intersection graphs of rings
let $r$ be a commutative ring with non-zero identity. we describe all $c_3$- and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. also, we shall describe all complete, regular and $n$-claw-free intersection graphs. finally, we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...
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The Fibonacci cube Γn is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1’s. The Lucas cube Λn is obtained 5 from Γn by removing vertices that start and end with 1. We characterize maximal induced hypercubes in Γn and Λn and deduce for any p ≤ n the number of maximal p-dimensional hypercubes in these graphs.
متن کاملLine graphs associated to the maximal graph
Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2003
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(02)00142-7