Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mapping... more Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mappingFfromX×XintoXand a mappinggfromXintoXwith some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalizedg-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalizedg-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.
Using inequalities is a good way of studying topological indices. Chemical graph theory is one of... more Using inequalities is a good way of studying topological indices. Chemical graph theory is one of the nontrivial applications of graph theory. In this paper, we examine and calculate another degreebased topological index for silicon-carbide structures. The Sombor index, which is a degree-based index, was introduced by Gutman in late 2020. In this paper, we first calculate and compare the Sombor index, then the decreasing Sombor index, and finally the mean Sombor index for a group of silicon-carbide structures.
Abstract: In this article, we have examined the Wiener index in neutrosophic graphs. Wiener index... more Abstract: In this article, we have examined the Wiener index in neutrosophic graphs. Wiener index is one of the most important topological indices. This index is a distance-based index that is calculated based on the geodesic distance between two vertices. Here, after defining the Wiener index in neutrosophic graphs, we calculated this index for some special modes such as the complete neutrosophic graph, cycle, and tree. In the following, by presenting a several theorems, we compared this index with the connectivity index, which is one of the most important degree-based indicators.
In the article, we review and critique the Corollary and Theorem of “Wiener index of a fuzzy grap... more In the article, we review and critique the Corollary and Theorem of “Wiener index of a fuzzy graph and application to illegal immigration networks”, and in addition to providing examples of violations.
International Journal of Nonlinear Analysis and Applications, 2021
In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $T$... more In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $T$ be a multivalued mappings on $X.$ Among other things, we obtain a fixed point of the mapping $T$ in the metric space $X$ endowed with a graph $G$ such that the set of vertices of $G,$ $V(G)=X$ and the set of edges of $G,$ $E(G)subseteq Xtimes X.$
International Journal of Nonlinear Analysis and Applications, 2016
In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,... more In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$
Neutrosophic Graphs are graphs that follow three-valued logic. They may be considered a fuzzy gra... more Neutrosophic Graphs are graphs that follow three-valued logic. They may be considered a fuzzy graph, although in some cases, it is difficult to optimize and model them using fuzzy graphs. In this paper, the first and second Zagreb indices, the Harmonic index, the Randic’ index and the Connectivity index for these graphs are investigated and some of the theorems related to these indices are discussed and proven. These indices are also calculated for some specific types of Neutrosophic Graphs, such as regular Neutrosophic Graphs and regular complete Neutrosophic Graphs.
Abstract: Connectivity is one of the most important concepts in graph theory. Since Neutrosophic ... more Abstract: Connectivity is one of the most important concepts in graph theory. Since Neutrosophic Graphs are a branch of graphs, connectivity will be very important in this branch as well. In this paper, we will define the connectivity in Neutrosophic graphs using the strength of connectedness between each pair of its vertices. Also in this article, we define two new concepts of Partial connectivity index and totally connectivity index. We present several theorems related to these concepts and prove the theorems.
In an article entitled The Counterexample of a theorem in “Wiener index of a fuzzy graph and appl... more In an article entitled The Counterexample of a theorem in “Wiener index of a fuzzy graph and application to illegal immigration networks”, we have shown a few examples of incorrect proof of a theorem in the Wiener index. Now, in this article, we will prove it by correcting the desired theorem. We have also used the same method as the author to prove it. There are other methods of proof.
Abstract The topological index has transformed the chemical structure into a numeric number and t... more Abstract The topological index has transformed the chemical structure into a numeric number and they make a connection between chemistry and mathematics. Kulli nominated the Banhatti index of a graph. In this paper, the four new operations of graphs based on the Indu-Bala product were computed according to the K Banhatti index.
In this paper, we first define the Neutrosophictree using the concept of the strong cycle. We the... more In this paper, we first define the Neutrosophictree using the concept of the strong cycle. We then define a strong spanning Neutrosophictree. In the following, we propose an algorithm for detecting the maximum spanning tree in Neutrosophicgraphs. Next, we discuss the Connectivity index and related theorems for Neutrosophictrees.
Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mapping... more Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mappingFfromX×XintoXand a mappinggfromXintoXwith some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalizedg-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalizedg-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.
Using inequalities is a good way of studying topological indices. Chemical graph theory is one of... more Using inequalities is a good way of studying topological indices. Chemical graph theory is one of the nontrivial applications of graph theory. In this paper, we examine and calculate another degreebased topological index for silicon-carbide structures. The Sombor index, which is a degree-based index, was introduced by Gutman in late 2020. In this paper, we first calculate and compare the Sombor index, then the decreasing Sombor index, and finally the mean Sombor index for a group of silicon-carbide structures.
Abstract: In this article, we have examined the Wiener index in neutrosophic graphs. Wiener index... more Abstract: In this article, we have examined the Wiener index in neutrosophic graphs. Wiener index is one of the most important topological indices. This index is a distance-based index that is calculated based on the geodesic distance between two vertices. Here, after defining the Wiener index in neutrosophic graphs, we calculated this index for some special modes such as the complete neutrosophic graph, cycle, and tree. In the following, by presenting a several theorems, we compared this index with the connectivity index, which is one of the most important degree-based indicators.
In the article, we review and critique the Corollary and Theorem of “Wiener index of a fuzzy grap... more In the article, we review and critique the Corollary and Theorem of “Wiener index of a fuzzy graph and application to illegal immigration networks”, and in addition to providing examples of violations.
International Journal of Nonlinear Analysis and Applications, 2021
In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $T$... more In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $T$ be a multivalued mappings on $X.$ Among other things, we obtain a fixed point of the mapping $T$ in the metric space $X$ endowed with a graph $G$ such that the set of vertices of $G,$ $V(G)=X$ and the set of edges of $G,$ $E(G)subseteq Xtimes X.$
International Journal of Nonlinear Analysis and Applications, 2016
In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,... more In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$
Neutrosophic Graphs are graphs that follow three-valued logic. They may be considered a fuzzy gra... more Neutrosophic Graphs are graphs that follow three-valued logic. They may be considered a fuzzy graph, although in some cases, it is difficult to optimize and model them using fuzzy graphs. In this paper, the first and second Zagreb indices, the Harmonic index, the Randic’ index and the Connectivity index for these graphs are investigated and some of the theorems related to these indices are discussed and proven. These indices are also calculated for some specific types of Neutrosophic Graphs, such as regular Neutrosophic Graphs and regular complete Neutrosophic Graphs.
Abstract: Connectivity is one of the most important concepts in graph theory. Since Neutrosophic ... more Abstract: Connectivity is one of the most important concepts in graph theory. Since Neutrosophic Graphs are a branch of graphs, connectivity will be very important in this branch as well. In this paper, we will define the connectivity in Neutrosophic graphs using the strength of connectedness between each pair of its vertices. Also in this article, we define two new concepts of Partial connectivity index and totally connectivity index. We present several theorems related to these concepts and prove the theorems.
In an article entitled The Counterexample of a theorem in “Wiener index of a fuzzy graph and appl... more In an article entitled The Counterexample of a theorem in “Wiener index of a fuzzy graph and application to illegal immigration networks”, we have shown a few examples of incorrect proof of a theorem in the Wiener index. Now, in this article, we will prove it by correcting the desired theorem. We have also used the same method as the author to prove it. There are other methods of proof.
Abstract The topological index has transformed the chemical structure into a numeric number and t... more Abstract The topological index has transformed the chemical structure into a numeric number and they make a connection between chemistry and mathematics. Kulli nominated the Banhatti index of a graph. In this paper, the four new operations of graphs based on the Indu-Bala product were computed according to the K Banhatti index.
In this paper, we first define the Neutrosophictree using the concept of the strong cycle. We the... more In this paper, we first define the Neutrosophictree using the concept of the strong cycle. We then define a strong spanning Neutrosophictree. In the following, we propose an algorithm for detecting the maximum spanning tree in Neutrosophicgraphs. Next, we discuss the Connectivity index and related theorems for Neutrosophictrees.
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Papers by Masoud Ghods