Dominator and total dominator colorings in vague graphs

Chen, Lian; Jiang, Huiqin; Shao, Zehui; Ivanović, Marija

doi:10.30538/psrp-easl2019.0017

Cited by 11 publications

(4 citation statements)

References 23 publications

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“…A molecular graph is a simple graph in which atoms and bonds are represented by vertex and edge sets, respectively. e vertex degree is the number of edges attached to that vertex [10][11][12][13][14][15][16]. e maximum degree of vertex among the vertices of a graph is denoted by Δ(G).…”

Section: Introductionmentioning

confidence: 99%

Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

Wang¹,

Chaudhry

Naseem

et al. 2020

Journal of Chemistry

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In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. Topological indices help us collect information about algebraic graphs and give us mathematical approach to understand the properties of algebraic structures. With the help of topological indices, we can guess the properties of chemical compounds without performing experiments in wet lab. ere are more than 148 topological indices in the literature, but none of them completely give all properties of under study compounds. Together, they do it to some extent; hence, there is always room to introduce new indices. In this paper, we present first and second reserve Zagreb indices and first reverse hyper-Zagreb indices, reverse GA index, and reverse atomic bond connectivity index for the crystallographic structure of molecules. We also present first and second reverse Zagreb polynomials and first and second reverse hyper-Zagreb polynomials for the crystallographic structure of molecules.

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Section: Introductionmentioning

confidence: 99%

Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

Wang¹,

Chaudhry

Naseem

et al. 2020

Journal of Chemistry

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“…. , m, j ≡ 0 mod n, the total labeling β is defined as: (Amal(fl n , {c}, m) Equations (12)(13)(14)(15)(16) altogether forms an arithmetic sequence with c = 12mn + 9 and common difference d = 1. This completes the proof.…”

Section: Super C 3 -Antimagic Labeling Of Amalgamation Of Flower Gmentioning

confidence: 99%

Amalgamations and Cycle-Antimagicness

et al. 2019

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A finite simple graph G is called a (c, d)-H-antimagic if G satisfies the following properties: (i) G has an H-covering by the family of subgraphs H 1 , H 2 ,. .. , H r where every H t ∼ = H , 1 ≤ t ≤ r, (ii) there exists a bijection β : V ∪ E → {1, 2, 3,. .. , |V ∪ E|} such that the H-weights constitute an arithmetic progression with initial term c and common difference d, where c > 0, d ≥ 0 are integers. The labeling β is called super if smallest possible labels appear on vertices of graph G. For m ∈ N and m ≥ 2, let {G i } m i=1 be a collection of graphs with u i ∈ V (G i) as a fixed vertex. The vertex amalgamation, denoted by Amal(G i , {u i }, m), is a graph formed by taking all the G i 's and identifying u i 's. In this research article, we studied super (c, 1) − C 3-antimagic labelings of amalgamation Amal(G i , {u i }, m) of wheels, fans and flower graphs.

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“…Fuzzy dominator colouring is essential in these applications. Frequently, in addition to the requirement that neighbouring vertices receive distinct colours, some extra colouring condition(s) must be met [2,3]. A graph is correct colouring is when colours are assigned to its vertices in such a way that no two neighbouring vertices accept the matching colour.…”

Section: Introductionmentioning

confidence: 99%

An Extensive Study on Graph Colourings and Dominator Chromatic Number of Sugeno-Type Fuzzy Graphs

Devi

2022

Mathematical Problems in Engineering

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The concept of graph colouring has become a very active field of research that enhances many practical applications and theoretical challenges. An accurate (vertex) colouring through the condition that each vertex is whichever unaccompanied in its colour class or adjoining to all vertices of at least one colour class is known as dominator colouring. A graph is dominator colouring is a suitable colouring in which at least one vertex dominates each colour class. Many difficult and global issues are solved using fuzzy graph colouring approaches. In this paper, we introduce a new Sugeno-Type Fuzzy graph of groups, which is found using several fuzzy graph operations such as dominant path-colouring number, cycle, union, join, and products. A number that is representative based on those vertices in the formations of all paths with those vertices as their starts and ends to compare with other paths is the minimum number of shared edges based on those vertices in the formations of all paths with those vertices as their starts and ends to compare with other paths. The sugeno dominant path-colouring number is the minimum Sugeno number of shared edges among the Sugeno cardinality of all sets of shared edges, which allows for various techniques. These results are used in studying various and recently introduced chromatic numbers of graphs.

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Dominator and total dominator colorings in vague graphs

Cited by 11 publications

References 23 publications

Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

Amalgamations and Cycle-Antimagicness

An Extensive Study on Graph Colourings and Dominator Chromatic Number of Sugeno-Type Fuzzy Graphs

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