Let  be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset  is a minimum neighborhood dominating set if  is a dominating set and if for every  holds. The minimum cardinality of the minimum neighborhood dominating set of a graph  is called as minimum neighborhood dominating number and it is denoted by  . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the

The local resolving neighborhood  of a pair of vertices  for  and  is if there is a vertex  in a connected graph  where the distance from  to  is not equal to the distance from  to , or defined by . A local resolving function  of  is a real valued function   such that  for  and . The local fractional metric dimension of graph  denoted by , defined by  In this research, the author discusses about the local fractional metric dimension of comb product are two graphs, namely graph  and graph , where graph  is a connected graphs and graph  is a complate graph &

The Detour distance is one of the most common distance types used in chemistry and computer networks today. Therefore, in this paper, the detour polynomials and detour indices of vertices identified of n-graphs which are connected to themselves and separated from each other with respect to the vertices for n≥3 will be obtained. Also, polynomials detour and detour indices will be found for another graphs which have important applications in Chemistry.

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 .

Activated carbon (AC) is a highly important adsorbent material, as it is a solid form of pure carbon that boasts a porous structure and a large surface area, making it effective for capturing pollutants. Thanks to its exceptional features, AC is widely used for purifying water that is contaminated with odors and removing dyes in a cost-effective manner. A variety of carbonic materials have been employed to prepare AC, and this study aimed to evaluate the suitability of utilizing waste mango and avocado seeds for this purpose, followed by testing their efficacy in removing dye from aqueous solutions. The results indicate that using waste mango and avocado as AC is technically feasible, achieving dye removal percentages of 98% and 93%,

In this ˑwork, we present theˑ notion of the ˑgraph for a KU-semigroup as theˑundirected simple graphˑ with the vertices are the elementsˑ of and weˑˑstudy the ˑgraph ofˑ equivalence classesˑofˑ which is determinedˑ by theˑ definition equivalenceˑ relation ofˑ these verticesˑ, andˑ then some related ˑproperties areˑ given. Several examples are presented and some theorems are proved. Byˑ usingˑ the definitionˑ ofˑ isomorphicˑ graph, ˑwe showˑ thatˑ the graphˑ of equivalence ˑclasses ˑand the ˑgraphˑof ˑa KU-semigroup ˑ areˑ theˑ sameˑ, in special cases.