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Papers by Ali Abu Dayah
Mathematics, 2019
The independent number of a graph G is the cardinality of the maximum independent set of G, denot... more The independent number of a graph G is the cardinality of the maximum independent set of G, denoted by α ( G ) . The independent dominating number is the cardinality of the smallest independent set that dominates all vertices of G. In this paper, we introduce a new class of graphs called semi-square stable for which α ( G 2 ) = i ( G ) . We give a necessary and sufficient condition for a graph to be semi-square stable, and we study when interval graphs are semi-square stable.
Open Mathematics, 2020
Given any digraph D, its non-negative spectrum (or N-spectrum, shortly) consists of the eigenvalu... more Given any digraph D, its non-negative spectrum (or N-spectrum, shortly) consists of the eigenvalues of the matrix AA T , where A is the adjacency matrix of D. In this study, we relate the classical spectrum of undirected graphs to the N-spectrum of their oriented counterparts, permitting us to derive spectral bounds. Moreover, we study the spectral effects caused by certain modifications of a given digraph.
Mathematics, 2019
The independent number of a graph G is the cardinality of the maximum independent set of G, denot... more The independent number of a graph G is the cardinality of the maximum independent set of G, denoted by α ( G ) . The independent dominating number is the cardinality of the smallest independent set that dominates all vertices of G. In this paper, we introduce a new class of graphs called semi-square stable for which α ( G 2 ) = i ( G ) . We give a necessary and sufficient condition for a graph to be semi-square stable, and we study when interval graphs are semi-square stable.
Open Mathematics, 2020
Given any digraph D, its non-negative spectrum (or N-spectrum, shortly) consists of the eigenvalu... more Given any digraph D, its non-negative spectrum (or N-spectrum, shortly) consists of the eigenvalues of the matrix AA T , where A is the adjacency matrix of D. In this study, we relate the classical spectrum of undirected graphs to the N-spectrum of their oriented counterparts, permitting us to derive spectral bounds. Moreover, we study the spectral effects caused by certain modifications of a given digraph.