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Tadpole Domination in Graphs
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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
Tue Jun 01 2021
Journal Name
Baghdad Science Journal
The Dominant Metric Dimension of Corona Product Graphs
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The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations. One of some concepts in graph theory that combine these two concepts is resolving dominating number. In this paper, the definition of resolving dominating number is presented again as the term dominant metric dimension. The aims of this paper are to find the dominant metric dimension of some special graphs and corona product graphs of the connected graphs  and , for some special graphs  . The dominant metric dimension of  is denoted by  and the dominant metric dimension of corona product graph G and H is denoted by .

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Publication Date
Mon Jan 30 2023
Journal Name
Iraqi Journal Of Science
More on Result Involution Graphs
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     The result involution graph of a finite group , denoted by  is an undirected simple graph whose vertex set is the whole group  and two distinct vertices are adjacent if their product is an involution element. In this paper, result involution graphs for all Mathieu groups and connectivity in the graph are studied. The diameter, radius and girth of this graph are also studied. Furthermore, several other graph properties are obtained.

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Publication Date
Wed Dec 26 2018
Journal Name
Iraqi Journal Of Science
Resultant Graphs of Block Designs
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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
Sat Sep 30 2023
Journal Name
Iraqi Journal Of Science
Further Results on Graceful Antimagic Graphs
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     Graceful labeling of a graph  with q edges is assigned the labels for its vertices by some integers from the set such that no two vertices received the same label, where each edge is assigned the absolute value of the difference between the labels of its end vertices and the resulting edge labeling running from 1 to  inclusive. An edge labeling of a graph G is called vertex anntimagic, if all vertex weights are pairwise distinct, where the vertex weight of a vertex under an edge labeling is the sum of the label of all edges incident with that vertex.  In this paper, we address the problem of finding graceful antimagic labelin for split of the star graph ,  graph,  graph, jellyfish graph , Dragon graph , ki

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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
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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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Publication Date
Tue Aug 01 2023
Journal Name
Baghdad Science Journal
Total Global Dominator Coloring of Trees and Unicyclic Graphs
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          A total global dominator coloring of a graph  is a proper vertex coloring of  with respect to which every vertex  in  dominates a color class, not containing  and does not dominate another color class. The minimum number of colors required in such a coloring of  is called the total global dominator chromatic number, denoted by . In this paper, the total global dominator chromatic number of trees and unicyclic graphs are explored.

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Publication Date
Mon Nov 19 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study of Two Types Finite Graphs in KU-Semigroups
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      In this Ë‘work, we present theË‘ notion of the Ë‘graph for a KU-semigroup  as theË‘undirected simple graphË‘ with the vertices are the elementsË‘ of  and weË‘Ë‘study the Ë‘graph ofË‘ equivalence classesË‘ofË‘  which is determinedË‘ by theË‘ definition equivalenceË‘ relation ofË‘ these verticesË‘, andË‘ then some related Ë‘properties areË‘ given. Several examples are presented and some theorems are proved. ByË‘ usingË‘ the definitionË‘ ofË‘ isomorphicË‘ graph, Ë‘we showË‘ thatË‘ the graphË‘ of equivalence Ë‘classes Ë‘and the Ë‘graphË‘of Ë‘a KU-semigroup Ë‘  areË‘ theË‘ sameË‘,

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Publication Date
Thu Dec 08 2022
Journal Name
Aequationes Mathematicae
On graceful antimagic graphs
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Publication Date
Thu Feb 01 2024
Journal Name
Baghdad Science Journal
Forgotten Index and Forgotten Coindex of Graphs
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F index is a connected graph, sum of the cubes of the vertex degrees. The forgotten topological index has been designed to be employed in the examination of drug molecular structures, which is extremely useful for pharmaceutical and medical experts in understanding the biological activities. Among all the topological indices, the forgotten index is based on degree connectivity on bonds. This paper characterized the forgotten index of union of graphs, join graphs, limits on trees and its complements, and accuracy is measured. Co-index values are analyzed for the various molecular structure of chemical compounds

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Publication Date
Wed Mar 01 2023
Journal Name
Baghdad Science Journal
Stability of Complement Degree Polynomial of Graphs
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     A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). A directed graph is a graph in which edges have orientation. A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex.  For a simple undirected graph G with order n, and let  denotes its complement. Let δ(G), ∆(G) denotes the minimum degree and maximum degree of G respectively. The complement degree polynomial of G is the polynomial CD[G,x]= , where C

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