On friendly index sets of 2-regular graphs

Kwong, Harris; Lee, Sin-Min; Ng, Ho Kuen

doi:10.1016/j.disc.2007.10.018

Cited by 21 publications

(8 citation statements)

References 8 publications

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“…In 2002, B.L.C hen etc expanded edge-balance multiple graph concept in reference [2], proved that the conjecture in reference [1] is true and obtained a graph is edge-balanced is not NP-difficult problem. In 2006-2008, Alexander, Harris, etc made a research of vertex-balanced index sets and friendly index sets in reference [3][4][5]. In 2008, Sub-Ryung used the structure method to study the new family of edge-balanced graph in reference [6].…”

Section: A Historymentioning

confidence: 99%

On the Edge-balanced Index Set of a class of Power-cycle Nested Network Graph

Zhang¹,

Zheng

2013

IJMECS

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Based on the research of Power-cycle Nested Graph , the decomposition method of single point sector has come up. By the use of the process of clawed nested-cycle sub-graph, the edge-balanced index sets of the power-cycle nested graph are solved when and . Besides, the constructive proofs of the computational formulas are also completed. The theory can be applied to information engineering, communication networks, computer science, economic management, medicine, etc. The proving method can be a reference to solve the problem of the power-cycle nested graph

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Section: A Historymentioning

confidence: 99%

On the Edge-balanced Index Set of a class of Power-cycle Nested Network Graph

Zhang¹,

Zheng

2013

IJMECS

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“…In [7], the friendly index sets of complete bipartite graphs and cycles are determined. In [5,6,8,9,10,11], the friendly index sets of other classes of graphs are determined. For further details of known results on friendly labelings and friendly index sets, the reader is directed to Gallian's [4] comprehensive survey of graph labelings.…”

Section: Introductionmentioning

confidence: 99%

On friendly index sets of k-galaxies

Lee¹,

Low

et al. 2019

ejgta

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Let G = (V, E) be a graph. A vertex labeling f : V → Z 2 induces an edge labeling f * : E → Z 2 defined by f * (xy) = f (x) + f (y), for each edge xy ∈ E. For i ∈ Z 2 , let v f (i) = |{v ∈ V : f (v) = i}| and e f (i) = |{e ∈ E : f * (e) = i}|. We say that f is friendly if |v f (1) − v f (0)| ≤ 1. The friendly index set of G, denoted by FI(G), is defined as FI(G) = {|e f (1) − e f (0)| : vertex labeling f is friendly}. A k-galaxy is a disjoint union of k stars. In this paper, we establish the friendly index sets for various classes of k-galaxies.

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“…The reference [2] extends the concept of edge-balanced labeling to multigraphs and completely characterizes the edge-balanced multigraphs, and proves the two conjectures are true in the reference [1], at the same time proves the problem of decide a graph is edge-balanced does not belong to NP-hard. In 2008, Alexander and Harris studied the vertex -balanced index and friendly index sets of the figure in the literature [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

On Computing the Edge-balanced Index Sets of the Circle Union Graph F (3, n)

Liu²

2016

IJMECS

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On the basis of power-cycle nested network graph, the edge-balanced index sets of circle union graph F(3,n) graph were investigated. A new method of changing index is provided, simplifying the proving process. It reduced the difficulty of circle union graph F(3,n) graph labeling because of the novel design of the basic graph and single-point sector subgraph. The results show that the edge-balanced index sets of circle union graph F(3,n) graph. This paper has proved the existence of the edge-balanced index sets of one class of circle union graph, the computational formulas and the construction of the corresponding graphs are also provided.

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On friendly index sets of 2-regular graphs

Cited by 21 publications

References 8 publications

On the Edge-balanced Index Set of a class of Power-cycle Nested Network Graph

On the Edge-balanced Index Set of a class of Power-cycle Nested Network Graph

On friendly index sets of k-galaxies

On Computing the Edge-balanced Index Sets of the Circle Union Graph F (3, n)

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