منابع مشابه
The total graph of a hypergraph
Let H be a hypergraph with vertices V(H) and hyperedges E(H). The total graph of H, T(H), is the simple graph with vertex set V(H)U E(H) where vertices x and y of T(H) are adjacent if and only if x is contained in, contains or is adjacent to y in H. We give a simple characterisation of those graphs which are the total graphs of some hypergraphs. We show that the total graph uniquely defines a l...
متن کاملA 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.
متن کاملTotal graph of a $0$-distributive lattice
Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${rm T}(G (£))$. It is the graph with all elements of £ as vertices, and for distinct $x, y in £$, the vertices $x$ and $y$ are adjacent if and only if $x vee y in {rm Z}(£)$. The basic properties of the ...
متن کاملZagreb Indices and Coindices of Total Graph, Semi-Total Point Graph and Semi-Total Line Graph of Subdivision Graphs
Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.
متن کاملComputing the atom graph of a graph and the union join graph of a hypergraph
The atom graph of a graph is the graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all possible atom trees of this graph. We provide two efficient algorithms for computing this atom graph, with a complexity in O(min(n log n, nm,n(n+m)) time, which is no more than the complexity of computing the atoms in the gene...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00230-0