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A note on the open packing number in graphs

Mehdi MohammadiMohammad Maghasedi — 2019

Mathematica Bohemica

A subset S of vertices in a graph G is an open packing set if no pair of vertices of S has a common neighbor in G . An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The maximum cardinality of an open packing set is called the open packing number and is denoted by ρ o ( G ) . A subset S in a graph G with no isolated vertex is called a total dominating set if any vertex of G is adjacent to some vertex of S . The total domination number of G , denoted...

On weakened ( α , δ ) -skew Armendariz rings

In this note, for a ring endomorphism α and an α -derivation δ of a ring R , the notion of weakened ( α , δ ) -skew Armendariz rings is introduced as a generalization of α -rigid rings and weak Armendariz rings. It is proved that R is a weakened ( α , δ ) -skew Armendariz ring if and only if T n ( R ) is weakened ( α ¯ , δ ¯ ) -skew Armendariz if and only if R [ x ] / ( x n ) is weakened ( α ¯ , δ ¯ ) -skew Armendariz ring for any positive integer n .

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