A Study of the Total Graph
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چکیده
Let R be a commutative ring with Z(R) its set of zero-divisors. In this paper, we study the total graph of R, denoted by T(Γ(R)). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y ∈ R, the vertices x and y are adjacent if and only if x + y ∈ Z(R). We study the chromatic number and edge connectivity of this graph.
منابع مشابه
A Study of the Total Graph
Let R be a commutative ring with $Z(R)$ its set of zero-divisors. In this paper, we study the total graph of $R$, denoted by $T(Gamma(R))$. It is the (undirected) graph with all elements of R as vertices, and for distinct $x, yin R$, the vertices $x$ and $y$ are adjacent if and only if $x + yinZ(R)$. We study the chromatic number and edge connectivity of this graph.
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تاریخ انتشار 2011