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Investigation of Commuting Graphs for Elements of Order 3 in Certain Leech Lattice Groups

      Assume that G is a finite group and X is a subset of G. The commuting graph is denoted by С(G,X) and has a set of vertices X with two distinct vertices x, y Î X, being connected together on the condition of xy = yx. In this paper, we investigate the structure of Ϲ(G,X) when G is a particular type of Leech lattice groups, namely Higman–Sims group HS and Janko group J2, along with  X as a G-conjugacy class of elements of order 3. We will pay particular attention to analyze the discs’ structure and determinate the diameters, girths, and clique number for these graphs.

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Publication Date
Sun Dec 09 2018
Journal Name
Baghdad Science Journal
Tadpole Domination in Graphs

A new type of the connected domination parameters called tadpole domination number of a graph is introduced. Tadpole domination number for some standard graphs is determined, and some bounds for this number are obtained. Additionally, a new graph, finite, simple, undirected and connected, is introduced named weaver graph. Tadpole domination is calculated for this graph with other families of graphs.

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Publication Date
Sun Mar 17 2019
Journal Name
Baghdad Science Journal
Hn-Domination in Graphs

The aim of this article is to introduce a new definition of domination number in graphs called hn-domination number denoted by . This paper presents some properties which show the concepts of connected and independent hn-domination. Furthermore, some bounds of these parameters are determined, specifically, the impact on hn-domination parameter is studied thoroughly in this paper when a graph is modified by deleting or adding a vertex or deleting an edge.

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Publication Date
Thu Feb 17 2022
Journal Name
Journal Of Discrete Mathematical Sciences And Cryptography
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Publication Date
Wed Mar 01 2023
Journal Name
Baghdad Science Journal
Quotient Energy of Zero Divisor Graphs And Identity Graphs

Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph  make up the graph's quotient energy. The objective of this study is to examine the quotient energy of identity graphs and zero-divisor graphs  of commutative rings using group theory, graph theory, and applications. In this study, the identity graphs  derived from the group  and a few classes of zero-divisor graphs  of the commutative ring R are examined.

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Publication Date
Thu Feb 17 2022
Journal Name
Journal Of Discrete Mathematical Sciences And Cryptography
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Publication Date
Fri Sep 30 2022
Journal Name
Iraqi Journal Of Science
Face Antimagic Labeling for Double Duplication of Barycentric and Middle Graphs

This paper proves the existence of face antimagic labeling for double duplication of barycentric subdivision of cycle and some other graphs 

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Publication Date
Wed Dec 26 2018
Journal Name
Iraqi Journal Of Science
Resultant Graphs of Block Designs

In this paper we have made different regular graphs by using block designs. In one of our applicable methods, first we have changed symmetric block designs into new block designs by using a method called a union method. Then we have made various regular graphs from each of them. For symmetric block designs with  (which is named finite projective geometry), this method leads to infinite class of regular graphs. With some examples we will show that these graphs can be strongly regular or semi-strongly regular. We have also propounded this conjecture that if two semi-symmetric block designs are non-isomorphic, then the resultant block graphs of them are non-isomorphic, too.

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Publication Date
Wed Feb 08 2023
Journal Name
Iraqi Journal Of Science
Investigation of Contaminated Bacteria and Some Toxic Elements of Groundwater in Some Wells in the Abu Ghraib Area/Baghdad

A total of 50 wells water samples were collected from 10 wells in Abu Ghraib site/ Baghdad for detection of coliform, fecal coliformand and pseudomonas aeruginosa bacteria, and the pollution of toxic ions (No3-, B+3, pb+2 and Cd+2 ) in wells water. Results showed microbial pollution by coliform, fecal Coliform bacteria in wells water when using presumptive, confirmed and complete tests, P. aeruginosa bacterium was isolated and identificated on Cetrimide Agar media, estimated the Most Probable Number (MPN) of coliforms and P. aeruginosa, results showed difference in mean of (MPN) of wells water. Most of toxic ions concentrations were low comparing with the recommended hygienic standards from the World Health Organization (WHO). Wells wate

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Publication Date
Sat Jan 30 2021
Journal Name
Iraqi Journal Of Science
A4-Graph of Finite Simple Groups

 

Let G be a finite group and X be a conjugacy class of order 3 in G. In this paper, we introduce a new type of graphs, namely A4-graph of  G, as a simple graph denoted by A4(G,X) which has X as a vertex set. Two vertices,  x and y, are adjacent if and only if  x≠y and  x y-1=y x-1. General properties  of the A4-graph as well as the structure of A4(G,X) when G@ 3D4(2) will be studied.

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Publication Date
Sun Nov 22 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Topological Structure of Generalized Rough Graphs

The main purpose of this paper, is to introduce a topological space , which is induced by reflexive graph and tolerance graph , such that  may be infinite. Furthermore, we offered some properties of  such as connectedness, compactness, Lindelöf and separate properties. We also study the concept of approximation spaces and get the sufficient and necessary condition that topological space is approximation spaces.

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