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Signpost systems and spanning trees of graphs

Ladislav Nebeský (2006)

Czechoslovak Mathematical Journal

By a ternary system we mean an ordered pair ( W , R ) , where W is a finite nonempty set and R W × W × W . By a signpost system we mean a ternary system ( W , R ) satisfying the following conditions for all x , y , z W : if ( x , y , z ) R , then ( y , x , x ) R and ( y , x , z ) R ; if x y , then there exists t W such that ( x , t , y ) R . In this paper, a signpost system is used as a common description of a connected graph and a spanning tree of the graph. By a ct-pair we mean an ordered pair ( G , T ) , where G is a connected graph and T is a spanning tree of G . If ( G , T ) is a ct-pair, then by the guide to...

Sobre un cono convexo asociado a un grafo.

Juan García Laguna (1984)

Trabajos de Estadística e Investigación Operativa

En este artículo se construye un cono convexo sobre un grafo y se estudian las propiedades básicas de este cono convexo: dimensión, linealidad y sistemas minimales de generadores. El interés de esta situación tiene su origen en problemas de decisión, donde la información disponible está dada por órdenes parciales entre las componentes de la información. Sin embargo, el estudio realizado es independiente de los problemas de decisión que lo motivan.

Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings

Mitra Jalali, Abolfazl Tehranian, Reza Nikandish, Hamid Rasouli (2020)

Commentationes Mathematicae Universitatis Carolinae

Let R be a commutative ring with identity and A ( R ) be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of R is defined as the graph SAG ( R ) with the vertex set A ( R ) * = A ( R ) { 0 } and two distinct vertices I and J are adjacent if and only if I Ann ( J ) ( 0 ) and J Ann ( I ) ( 0 ) . In this paper, the perfectness of SAG ( R ) for some classes of rings R is investigated.

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