Edge-gracefulness of the composition of paths with null graphs

Wai Chee SHIU; Peter Che Bor Lam; Hee Lin Cheng

doi:10.1016/S0012-365X(01)00449-6

Edge-gracefulness of the composition of paths with null graphs

Wai Chee SHIU^*
, Peter Che Bor Lam
, Hee Lin Cheng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

12 Citations (Scopus)

32 Downloads (Pure)

Abstract

Let G = (V,E) be a (p,q)-graph. Let f:E → {1,2,...,9} be a bijection. The induced mapping f+ : V→_p of / is defined by f⁺(M) = σ_urεE;/(uv) (modp) for i/£ V. If /+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs P_m o N_n, where there are mn vertices and (m -1 )n2 edges. We show that P) o N is edge-graceful if H is odd.

Original language	English
Pages (from-to)	63-76
Number of pages	14
Journal	Discrete Mathematics
Volume	253
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(01)00449-6
Publication status	Published - 6 Jun 2002

User-Defined Keywords

Composition of graph
Edge-graceful
Labeling matrix

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title = "Edge-gracefulness of the composition of paths with null graphs",

abstract = "Let G = (V,E) be a (p,q)-graph. Let f:E → \{1,2,...,9\} be a bijection. The induced mapping f+ : V→p of / is defined by f+(M) = σurεE;/(uv) (modp) for i/£ V. If /+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs Pm o Nn, where there are mn vertices and (m -1 )n2 edges. We show that P) o N is edge-graceful if H is odd.",

keywords = "Composition of graph, Edge-graceful, Labeling matrix",

author = "SHIU, \{Wai Chee\} and Lam, \{Peter Che Bor\} and Cheng, \{Hee Lin\}",

note = "Funding Information: Partially supported by RGC, Hong Kong; and FRG, Hong Kong Baptist University. ∗Corresponding author. E-mail address: [email protected] (W.C. Shiu).",

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T1 - Edge-gracefulness of the composition of paths with null graphs

AU - SHIU, Wai Chee

AU - Lam, Peter Che Bor

AU - Cheng, Hee Lin

N1 - Funding Information: Partially supported by RGC, Hong Kong; and FRG, Hong Kong Baptist University. ∗Corresponding author. E-mail address: [email protected] (W.C. Shiu).

PY - 2002/6/6

Y1 - 2002/6/6

N2 - Let G = (V,E) be a (p,q)-graph. Let f:E → {1,2,...,9} be a bijection. The induced mapping f+ : V→p of / is defined by f+(M) = σurεE;/(uv) (modp) for i/£ V. If /+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs Pm o Nn, where there are mn vertices and (m -1 )n2 edges. We show that P) o N is edge-graceful if H is odd.

AB - Let G = (V,E) be a (p,q)-graph. Let f:E → {1,2,...,9} be a bijection. The induced mapping f+ : V→p of / is defined by f+(M) = σurεE;/(uv) (modp) for i/£ V. If /+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs Pm o Nn, where there are mn vertices and (m -1 )n2 edges. We show that P) o N is edge-graceful if H is odd.

KW - Composition of graph

KW - Edge-graceful

KW - Labeling matrix

UR - https://www.scopus.com/pages/publications/33749615477

U2 - 10.1016/S0012-365X(01)00449-6

DO - 10.1016/S0012-365X(01)00449-6

M3 - Journal article

AN - SCOPUS:33749615477

SN - 0012-365X

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SP - 63

EP - 76

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

Edge-gracefulness of the composition of paths with null graphs

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