Edge Roman Star Domination Number on Graphs

Sinha, Angshu Kumar; Rana, Akul; Pal, Anita

doi:10.22457/apam.v14n1a17

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Illustration Of Algorithm L2111

Introduction1

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2021

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“…Res. 13 (2), 537-544 (2021) 543 Iteration 4: j = 5. L 1 (F 5 ) = {1, 3}, L 2 (F 5 ) = {0, 2}, L 3 (F 5 ) =  .…”

Section: Illustration Of Algorithm L211mentioning

confidence: 99%

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L(2,1,1)-Labeling of Circular-Arc Graphs

Amanathulla¹,

Bera

Pal³

2021

J. Sci. Res.

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Graph labeling problem has been broadly studied in recent past for its wide applications, in mobile communication system for frequency assignment, radar, circuit design, X-ray crystallography, coding theory, etc. An L211-labeling (L211L) of a graph G = (V, E) is a function γ : V → Z∗ such that |γ(u) − γ(v)| ≥ 2, if d(u, v) = 1 and |γ(u) − γ(v)| ≥ 1, if d(u, v) = 1 or 2, where Z∗ be the set of non-negative integers and d(u, v) represents the distance between the nodes u and v. The L211L numbers of a graph G, are denoted by λ2,1,1(G) which is the difference between largest and smallest labels used in L211L. In this article, for circular-arc graph (CAG) G we have proved that λ2,1,1(G) ≤ 6∆ − 4, where ∆ represents the degree of the graph. Beside this we have designed a polynomial time algorithm to label a CAG satisfying the conditions of L211L. The time complexity of the algorithm is O(n∆2), where n is the number of nodes of the graph G.

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“…Res. 13 (2), 537-544 (2021) 543 Iteration 4: j = 5. L 1 (F 5 ) = {1, 3}, L 2 (F 5 ) = {0, 2}, L 3 (F 5 ) =  .…”

Section: Illustration Of Algorithm L211mentioning

confidence: 99%

“…are studied by many researchers. Nowadays graph domination problem is an important problem of graph theory [2].…”

Section: Introductionmentioning

confidence: 99%