3-total edge mean cordial labeling of some standard graphs

Aslam, Fakhir; Zahid, Zohaib; Zafar, Sohail

doi:10.30538/oms2019.0056

Cited by 12 publications

(7 citation statements)

References 8 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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“…Figure (2) shows an example of 4C 7 -path. Theorem 1: For integers m ≥ 2 and n ≥ 3, the mC n -path is super (c, 1)-C n -antimagic.…”

Section: Super Cycle-antimagic Labeling Of Chain Graphmentioning

confidence: 99%

Antimagicness of $mC_n$ -Path and Its Disjoint Union

Umar²,

Habib

et al. 2019

IEEE Access

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Let M = (V (M), E(M)) be a simple graph with finite vertices and edges. An N-covering of M is a family {N 1 , N 2 ,. .. , N α } of subgraphs of M isomorphic to N such that every edge in E(M) belongs to N l , for some l, l ∈ {1, 2,. .. , α}. Such a graph is a (c, d)-N-antimagic if ∃ a bijection ψ : V M ∪E M → {1, 2,. .. , |V M |+|E M |} such that for all N l ∼ = N , {wt ψ (N l)} = {c, c+d,. .. , c+(α −1)d}. For ψ(V (M)) = {1, 2, 3,. .. , |V (M)|}, the labeling ψ would be super (c, d)-N-antimagic and for d = 0 it would be N-supermagic. In this manuscript, we investigated that mC n-path has super (c, d)-C n-antimagic labeling for differences d ∈ {0, 1,. .. , 5} and extend the result for C n-supermagic labeling of disjoint union of isomorphic copies of mC n-path. INDEX TERMS Block cut-vertex graph, mC n-path, disjoint union of mC n-path, super (c, d)-C n-antimagic.

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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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3-total edge mean cordial labeling of some standard graphs

Abstract: In this paper, we introduce new labeling and named it as k-total edge mean cordial (k-TEMC) labeling. We study certain classes of graphs namely path, double comb, ladder and fan in the context of 3-TEMC labeling.

Cited by 12 publications

References 8 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

Antimagicness of $mC_n$ -Path and Its Disjoint Union

Amalgamations and Cycle-Antimagicness

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