Radio mean labeling of a graph

Ponraj, R.; Narayanan, S. Sathish; Kala, R.

doi:10.1016/j.akcej.2015.11.019

Cited by 19 publications

(9 citation statements)

References 6 publications

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“…Definition 2.14. [7] The Sunflower SF n is obtained from a wheel W n with the central vertex w 0 and cycle…”

Section: Resultsmentioning

confidence: 99%

Neighbourhood $V_4-$magic labeling of some subdivision graphs

Vineesh¹,

Kumar²

2020

Malaya J. Mat

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Let V 4 = {0, a, b, c} be the Klein-4-group with identity element 0.A graph G = (V (G), E(G)),with vertex set V (G) and edge set E(G), is said to be Neighbourhood V 4-magic if there exists a labeling f : V (G) → V 4 \{0} such that the sum N + f (v) = ∑ u∈N(v) f (u) is a constant map. If this constant is p,where p is any non zero element in V 4 ,then we say that f is a p-neighbourhood V 4-magic labeling of G and G is said to be a p-neighbourhood V 4-magic graph. If this constant is 0,then we say that f is a 0-neighbourhood V 4-magic labeling of G and G is said to be a 0-neighbourhood V 4-magic graph. Keywords Klein-4-group, a-neighbourhood V 4-magic graphs and 0-neighbourhood V 4-magic graphs.

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“…Definition 2.14. [7] The Sunflower SF n is obtained from a wheel W n with the central vertex w 0 and cycle…”

Section: Resultsmentioning

confidence: 99%

Neighbourhood $V_4-$magic labeling of some subdivision graphs

Vineesh¹,

Kumar²

2020

Malaya J. Mat

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“…Ponraja et al [8][9] proposed the radio mean labeling of graphs as follows: let h be an injective function from the vertex set, , to the set of natural numbers where where for any two distinct vertices and of the graph G, ⌈ ⌉ , where diam is the diameter of G and d(x, y) denotes the distance between the two vertices x and y. The number of radio mean of , , is the maximum number assigned to any vertex of .…”

Section: Letmentioning

confidence: 99%

“…The number of radio mean of , , is the minimum value of , taken over all radio mean labeling of . Ponraja et al [8] found the number of radio mean for networks with diameter 3, lotus with a circle, Sunflower networks and Helms. Ponraja and Sathish [9] determined the number of radio mean for some networks that are related to cycles and complete graph.…”

Section: Letmentioning

confidence: 99%

“…Ponraja et al [8] found the number of radio mean for networks with diameter 3, lotus with a circle, Sunflower networks and Helms. Ponraja and Sathish [9] determined the number of radio mean for some networks that are related to cycles and complete graph. In [10] they found the number of radio mean for triangular ladder network, ̅ (It consists of a path P n in which every vertex x i joined to two vertices y i and z i of ̅ , ̅ (It consists of a complete graph K n in which every vertex x i joined to two vertices y i and z i of ̅ and ̅ (It consists of a wheel W n in which every vertex x i joined to two vertices y i and z i of ̅ .…”

Section: Letmentioning

confidence: 99%

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An Integer Linear Programming Model for Solving Radio Mean Labeling Problem

et al. 2020

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A Radio mean labeling of a connected graph is an injective function from the vertex set, , to the set of natural numbers such that for any two distinct vertices and of , ⌈ ⌉. The radio mean number of , , is the maximum number assigned to any vertex of. The radio mean number of , , is the minimum value of , taken over all radio mean labeling of. This work has three contributions. The first one is proving two theorems which find the radio mean number for cycles and paths. The second contribution is proposing an approximate algorithm which finds an upper bound for radio mean number of a given graph. The third contribution is that we introduce a novel integer linear programing formulation for the radio mean problem. Finally, the experimental results analysis and statistical test proved that the Integer Linear Programming Model overcame the proposed approximate algorithm according to CPU time only. On the other hand, both the Integer Linear Programming Model and the proposed approximate algorithm had the same upper bound of the radio mean number of G.

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“…Radio mean labeling was introduced by R. Ponraj et al [14,15,16]. A radio mean labeling is a one to one mapping from V(G) to ℕ satisfying the condition…”

Section: Introductionmentioning

confidence: 99%

On Radio Mean D-Distance Number of Graph Obtained from Graph Operation

las¹,

Bosco²,

ola³

2018

IJMTT

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A Radio Mean D-distance labeling of a connected graph G is an injective map f from the vertex set V(G) to ℕ such that for two distinct vertices u and v of G, d D (u, v) + + () 2 ≥ 1 + diam D (G), where d D (u, v) denotes the D-distance between u and v and diam D (G) denotes the D-diameter of G. The radio mean Ddistance number of f, rmn D (f) is the maximum label assigned to any vertex of G. The radio mean D-distance number of G, rmn D (G) is the minimum value of rmn D (f) taken over all radio mean D-distance labeling f of G. In this paper we find the radio mean D-distance number of graph obtained from graph operation.

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Radio mean labeling of a graph

Cited by 19 publications

References 6 publications

Neighbourhood $V_4-$magic labeling of some subdivision graphs

Neighbourhood $V_4-$magic labeling of some subdivision graphs

An Integer Linear Programming Model for Solving Radio Mean Labeling Problem

On Radio Mean D-Distance Number of Graph Obtained from Graph Operation

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