L(2, 1)-Labeling of Permutation and Bipartite Permutation Graphs

Paul, Satyabrata; Pal, Madhumangal; Pal, Anita

doi:10.1007/s11786-014-0180-2

Cited by 18 publications

(11 citation statements)

References 29 publications

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“…Firstly, we establish the lower and upper bound. [8,10,12,14,18,16,13,11,9,7,3,5], A 6 = [8,10,12,14,17,19,15,13,11,9,7,3,5]. Now we give an L(2, 1)-labeling of C 2 n with edge span 6, as shown in Table 1.…”

Section: The L(2 1) Edge Span Of the Square Of A Cyclementioning

confidence: 99%

“…So it is not possible to compute λ-number of a graph in polynomial time unless P = NP. Therefore, the problem has been studied for many special classes of graphs, such as regular grids [1,2], product graphs [10,14], trees [4,18], planar graphs [17], generalized flowers [11], permutation and bipartite permutation graphs [15] and so on. For more details, one may refer to the surveys [3,19].…”

Section: Introductionmentioning

confidence: 99%

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Distance Two Labeling on the Square of a Cycle

ZHANG

2015

Korean Journal of Mathematics

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Abstract. An L(2, 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers such thatThe λ-number of G, denoted λ(G), is the smallest number k such that G admits an L(2, 1)-labeling with k = max{f (u)|u ∈ V (G)}. In this paper, we consider the square of a cycle and provide exact value for its λ-number. In addition, we also completely determine its edge span.

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Section: The L(2 1) Edge Span Of the Square Of A Cyclementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distance Two Labeling on the Square of a Cycle

ZHANG

2015

Korean Journal of Mathematics

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“…e intersection graphs or networks [1,2] form a large family of structures which include many important network such as interval [3,4], permutation [5,6], chordal [7,8], circular-arc [9,10], circle [11], string [12], line [13,14], and path [15,16]. Most of these networks are of great significance not only theoretically but because of their applicability in the fields such as transportation [17], wireless networking [18], scheduling problem [19], molecular biology [20], circuit routing [21], and sociology.…”

Section: Introductionmentioning

confidence: 99%

Characterization of 2-Path Signed Network

Sinha

Sharma

2020

Complexity

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A signed network is a network where each edge receives a sign: positive or negative. In this paper, we report our investigation on 2-path signed network of a given signed network Σ , which is defined as the signed network whose vertex set is that of Σ and two vertices in Σ 2 are adjacent if there exist a path of length two between them in Σ . An edge ab in Σ 2 receives a negative sign if all the paths of length two between them are negative, otherwise it receives a positive sign. A signed network is said to be if clusterable its vertex set can be partitioned into pairwise disjoint subsets, called clusters, such that every negative edge joins vertices in different clusters and every positive edge joins vertices in the same clusters. A signed network is balanced if it is clusterable with exactly two clusters. A signed network is sign-regular if the number of positive (negative) edges incident to each vertex is the same for all the vertices. We characterize the 2-path signed graphs as balanced, clusterable, and sign-regular along with their respective algorithms. The 2-path network along with these characterizations is used to develop a theoretic model for the study and control of interference of frequency in wireless communication networks.

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“…For some applications of this graph class see chapter 7 of the book [7]. Some researchers [3,23] investigated L(2, 1)-labelling of this graph classes. But, there are very few works on L(0, 1)-labelling of permutation graphs.…”

Section: Introductionmentioning

confidence: 99%

L(0,1)-labelling of Permutation Graphs

Paul

Pal

2015

J Math Model Algor

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L(0, 1)-labelling of a graph G = (V , E) is a function f from the vertex set V (G) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The goal of L(0, 1)-labelling problem is to produce a legal labelling that minimize the largest label used. In this article, it is shown that, for a permutation graph G with maximum vertex degree , the upper bound of λ 0,1 (G) is − 1. Finally, we prove that the result is exact for bipartite permutation graph.

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L(2, 1)-Labeling of Permutation and Bipartite Permutation Graphs

Cited by 18 publications

References 29 publications

Distance Two Labeling on the Square of a Cycle

Distance Two Labeling on the Square of a Cycle

Characterization of 2-Path Signed Network

L(0,1)-labelling of Permutation Graphs

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