The partition dimension of a complete multipartite graph, a special caterpillar and a windmill

S. Uttunggadewa; R. Simanjuntak; E. T. Baskoro

The partition dimension of a complete multipartite graph, a special caterpillar and a windmill

Darmaji^*, S. Uttunggadewa, R. Simanjuntak, E. T. Baskoro

^*Corresponding author for this work

Laboratory of Programming and Visual Computing

Bandung Institute of Technology

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

In this paper, we determine the partition dimension of a complete multipartite graph K_n1,n₂,... .n_r, namely pd(K_n1,n₂,... .n_r,) isr + n- 1 if n_i = n for 1 ≤ i ≤ r and pd(K_n1,n₂,... .n_r) is r + n - 2 for n = n₁ ≥ n₂ ≥ ≥ n_r. We also show that the partition dimension of caterpillar graph C _n^m is m for n ≤ m and m + 1 for n > m, and the partition dimension of windmill graph W₂^m is k, where k is the smallest integer such that (k/2) ≥ m.

Original language	English
Pages (from-to)	209-215
Number of pages	7
Journal	Journal of Combinatorial Mathematics and Combinatorial Computing
Volume	71
Publication status	Published - Nov 2009

Keywords

Caterpillar
Complete multipartite graph
Partition dimension
Resolving partition
Windmill graph

Cite this

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abstract = "In this paper, we determine the partition dimension of a complete multipartite graph Kn1,n2,... .nr, namely pd(Kn1,n2,... .nr,) isr + n- 1 if ni = n for 1 ≤ i ≤ r and pd(Kn1,n2,... .nr) is r + n - 2 for n = n1 ≥ n2 ≥ ≥ nr. We also show that the partition dimension of caterpillar graph C nm is m for n ≤ m and m + 1 for n > m, and the partition dimension of windmill graph W2m is k, where k is the smallest integer such that (k/2) ≥ m.",

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AU - Darmaji,

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AU - Simanjuntak, R.

AU - Baskoro, E. T.

PY - 2009/11

Y1 - 2009/11

N2 - In this paper, we determine the partition dimension of a complete multipartite graph Kn1,n2,... .nr, namely pd(Kn1,n2,... .nr,) isr + n- 1 if ni = n for 1 ≤ i ≤ r and pd(Kn1,n2,... .nr) is r + n - 2 for n = n1 ≥ n2 ≥ ≥ nr. We also show that the partition dimension of caterpillar graph C nm is m for n ≤ m and m + 1 for n > m, and the partition dimension of windmill graph W2m is k, where k is the smallest integer such that (k/2) ≥ m.

AB - In this paper, we determine the partition dimension of a complete multipartite graph Kn1,n2,... .nr, namely pd(Kn1,n2,... .nr,) isr + n- 1 if ni = n for 1 ≤ i ≤ r and pd(Kn1,n2,... .nr) is r + n - 2 for n = n1 ≥ n2 ≥ ≥ nr. We also show that the partition dimension of caterpillar graph C nm is m for n ≤ m and m + 1 for n > m, and the partition dimension of windmill graph W2m is k, where k is the smallest integer such that (k/2) ≥ m.

KW - Caterpillar

KW - Complete multipartite graph

KW - Partition dimension

KW - Resolving partition

KW - Windmill graph

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M3 - Article

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SN - 0835-3026

VL - 71

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JO - Journal of Combinatorial Mathematics and Combinatorial Computing

JF - Journal of Combinatorial Mathematics and Combinatorial Computing

ER -

The partition dimension of a complete multipartite graph, a special caterpillar and a windmill

Abstract

Keywords

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