Consecutive-magic labeling of generalized Petersen graphs

Martin Bača

Consecutive-magic labeling of generalized Petersen graphs

Martin Bača

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Abstract

The generalized Petersen graph P(n, k) has vertex set V = { u₁ , u₂ , . . . , u_n , v₁ , v₂ , . . . , v_n } and edge set E = { u_i u_{i + 1} , u_i v_i , v_i v_{i + k} \ for 1 ≤ i ≤ n and 1 ≤ k ≤ [n-1/2], with indices taken modulo n}. We deal with the problem of labeling edges of the generalized Petersen graph P(n, k) and we show that P(n, k) is consecutive-magic iff n is even (n ≥ 4) and k ≤ n/2 - 1.

Original language	English
Pages (from-to)	237-241
Number of pages	5
Journal	Utilitas Mathematica
Volume	58
State	Published - Nov 2000

Cite this

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title = "Consecutive-magic labeling of generalized Petersen graphs",

abstract = "The generalized Petersen graph P(n, k) has vertex set V = \{ u1 , u2 , . . . , un , v1 , v2 , . . . , vn \} and edge set E = \{ ui ui + 1 , ui vi , vi vi + k \textbackslash{} for 1 ≤ i ≤ n and 1 ≤ k ≤ [n-1/2], with indices taken modulo n\}. We deal with the problem of labeling edges of the generalized Petersen graph P(n, k) and we show that P(n, k) is consecutive-magic iff n is even (n ≥ 4) and k ≤ n/2 - 1.",

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N2 - The generalized Petersen graph P(n, k) has vertex set V = { u1 , u2 , . . . , un , v1 , v2 , . . . , vn } and edge set E = { ui ui + 1 , ui vi , vi vi + k \ for 1 ≤ i ≤ n and 1 ≤ k ≤ [n-1/2], with indices taken modulo n}. We deal with the problem of labeling edges of the generalized Petersen graph P(n, k) and we show that P(n, k) is consecutive-magic iff n is even (n ≥ 4) and k ≤ n/2 - 1.

AB - The generalized Petersen graph P(n, k) has vertex set V = { u1 , u2 , . . . , un , v1 , v2 , . . . , vn } and edge set E = { ui ui + 1 , ui vi , vi vi + k \ for 1 ≤ i ≤ n and 1 ≤ k ≤ [n-1/2], with indices taken modulo n}. We deal with the problem of labeling edges of the generalized Petersen graph P(n, k) and we show that P(n, k) is consecutive-magic iff n is even (n ≥ 4) and k ≤ n/2 - 1.

UR - https://www.scopus.com/pages/publications/0034343892

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SP - 237

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JO - Utilitas Mathematica

JF - Utilitas Mathematica

ER -

Consecutive-magic labeling of generalized Petersen graphs

Abstract

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