On the $k$-distant total labeling of graphs

Rana, Akul

doi:10.26637/mjm0802/0040

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2021

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“…Also, Amanathulla et al shown that λ 0,1 (G) ≤ ∆ and λ 1,1 (G) ≤ 2∆ for CAGs [10]. In 2020, Rana have studied graph a new variation of graph labeling problem [3,4]. Also, in 2020, Amanathulla et al have studied L(3,2,1)-labeling of trapezoid graph and obtained good result for it [18].…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%