arXiv subjects

Reza Jafarpour-Golzari

Publications and source records attributed to Reza Jafarpour-Golzari.

6 recordsLinked to original sources

arXiv2021

On well-f-coveredness of lexicographic product of graphs

A simple graph G is said to be well-f-covered, whenever any two maximal induced forest in G be of the same order. In this note, well-f-coveredness of lexicographic product of two graphs in case where the first component is empty, is characterized. In cases where the second component is empty, and the second component is nonempty, a necessary condition is given, and in each one, by an example, it is shown that the given condition is not sufficient.

math.CO↗

arXiv2021

Graphs whose all maximal induced forests are of the same order

In this paper, a new concept in graphs namely well-f-coveredness is introduced. We characterize all graphs with such property, whose maximum induced forests are of boundary order. Also we prove several propositions concerning with obtaining large well-f-covered graphs from smaller ones. By the way, some interesting classes of well-f-covered graphs are characterized.

math.CO↗

arXiv2020

Degree polynomial of vertices in a graph and its behavior under graph operations

In this paper, we introduce a new concept namely degree polynomial for vertices of a simple graph. This notion leads to a concept namely degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the degree polynomial sequence for some well-known graphs, we prove a theorem which gives a necessary condition for realizability of a sequence of polynomials with coefficients in positive integers. Also we calculate the degree polynomial for vertises of join, Cartesian product, tensor product, and lexicographic product of two simple graphs and for vertices of the complement of a simple graph. Some examples, counterexamples, and open problems concerning to this subjects, is given as well

math.CO↗

arXiv2016

A generalization of hall's theorem for k-uniform k-partite hypergraphs

In this paper we prove a generalized version of Hall's theorem for hypergraphs. More precisely, let H be a k-uniform k- partite hypergraph with some ordering on parts as V1, V2,..., Vk. such that the subhypergraph generated on union of V1, V2,..., Vk-1 has a unique perfect matching. In this case, we give a necessary and sufficient condition for having a matching of size t = |V1| in H. Some relevant results and counterexamples are given as well.

math.CO↗

arXiv2016

Unmixed d-uniform r-partite hypergraphs

In this paper, we characterize all unmixed d-uniform r-partite hypergraphs under a certain condition. Also we give a necessary condition for unmixedness in d-uniform hypergraphs with a perfect matching of size n. Finally we give a sufficient condition for unmixednes in d-uniform hypergraphs with a perfect matching.

math.AC↗

arXiv2015

$P_{Z}(S)$-Metrics and $P_{Z}(S)$-Metric Spaces

In this paper, we define notions of $P_{Z}(S)$-metric and $P_{Z}(S)$-metric space and we show that every $P_{Z}(S)$-metric Space, analogous to an ordinary metric space and generally, a $Λ$-metric space, is a topological space, and in continuance, we show that from a topological point of view, some properties of $P_{Z}(S)$-metric spaces, and $Λ$-metric spaces, have coordination.

math.GN↗