Multi-level and antipodal labelings for certain classes of circulant graphs

Topological indices and polynomials are predicting properties like boiling points, fracture toughness, heat of formation, etc., of different materials, and thus save us from extra experimental burden. In this article we compute many topological indices for the family of circulant graphs. At first, we give a general closed form of M-polynomial of this family and recover many degree-based topological indices out of it. We also compute Zagreb indices and Zagreb polynomials of this family. Our results extend many existing results.

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“…computed the revised Szeged spectrum of circulant graphs [28]. Multi-level and antipodal labelings for circulant graphs is discussed in [29,30].…”

Section: Graphmentioning

confidence: 99%

Some Invariants of Circulant Graphs

et al. 2016

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“…William and Robert, [24] obtained an upper bound for the radio antipodal number of the hexagonal mesh and grid. The radio antipodal number of the Circulant graph was studied in [25,26]. In this paper, the antipodal number of Mongolian tents and Torus grid has been studied.…”

Section: Introductionmentioning

confidence: 99%

Radio Antipodal Labeling of Mongolian Tent and Torus Grid Graphs

Gomathi,

Venugopal,

Jose

2023

Ars Comb.

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An antipodal labeling is a function f from the vertices of G to the set of natural numbers such that it satisfies the condition d ( u , v ) + | f ( u ) – f ( v ) | ≥ d , where d is the diameter of G and d ( u , v ) is the shortest distance between every pair of distinct vertices u and v of G . The span of an antipodal labeling f is s p ( f ) = max { | f ( u ) – f ( v ) | : u , v ∈ V ( G ) } . The antipodal number of~G, denoted by~an(G), is the minimum span of all antipodal labeling of~G. In this paper, we determine the antipodal number of Mongolian tent and Torus grid.

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“…Graph labeling has been used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management [10][11][12]. In the present article, we have studied super T (4,2) -antimagic labeling of web graphs W(2, n) for differences d ∈ 0, 1, .…”

Section: Introductionmentioning

confidence: 99%

Tree-Antimagicness of Web Graphs and Their Disjoint Union

Zhang

Umar²,

Ren

et al. 2020

Mathematical Problems in Engineering

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In graph theory, the graph labeling is the assignment of labels (represented by integers) to edges and/or vertices of a graph. For a graph G=V,E, with vertex set V and edge set E, a function from V to a set of labels is called a vertex labeling of a graph, and the graph with such a function defined is called a vertex-labeled graph. Similarly, an edge labeling is a function of E to a set of labels, and in this case, the graph is called an edge-labeled graph. In this research article, we focused on studying super ad,d-T4,2-antimagic labeling of web graphs W2,n and isomorphic copies of their disjoint union.

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Multi-level and antipodal labelings for certain classes of circulant graphs

Abstract: A radio k-labeling c of a graph G is a mapping c

Cited by 4 publications

References 6 publications

Some Invariants of Circulant Graphs

Some Invariants of Circulant Graphs

Radio Antipodal Labeling of Mongolian Tent and Torus Grid Graphs

Tree-Antimagicness of Web Graphs and Their Disjoint Union

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