# Combination labelings of graphs related to several cycles and paths

## Authors

• Aiewcharoen Busakorn Silpakorn University.
• Ratinan Boonklurb Chulalongkorn University.
• Sakulwat Promvichitkul Chulalongkorn University.

## Keywords:

graph labeling, combinatorial labeling, cycle, path

## Abstract

Suppose that G = (V (G), E(G)) is a graph and |V (G)| = p. If there exists a bijective function f : V (G) → {1, 2, 3, ..., p} such that an f c : E(G) → N defined by f c(uv) = (f(u)f(v))when f (u) > f(v) and f c(uv) = (f(u)f(v))when f (v) > f (u) is an injection function, then f  is called a combination labelings and G is called a combination graph.

This article considers a suitable bijective function f and prove that G(Cn, Cm, Pk) which are graphs related to two cycles and one path containing three parameters, are combination graphs.

## Author Biographies

### Aiewcharoen Busakorn, Silpakorn University.

Demonstration School of Silpakorn University, Faculty of Education.

### Ratinan Boonklurb, Chulalongkorn University.

Department of Mathematics and Computer Science, Faculty of Science.

### Sakulwat Promvichitkul, Chulalongkorn University.

Department of Mathematics and Computer Science, Faculty of Science.

## References

J. A. Gallian, “A dynamic survey of graph labelings”, The Electronic Journal of Combinatorics, vol. 16, 2009.

M. S. Hegde and S. Shetty, “Combinatorial labelings of graphs”, Applied Mathematics E-note, vol. 6, pp. 251-258, 2006.

P. C. Li, “Combination labelings of graphs”, Applied Mathematics E-note, vol. 12, pp. 158-168, 2012. [On line]. Available: https://bit.ly/3AuNvns

K. Thitiwatthanakan and S. Leeratanavalee, “Combinatorial Labelings of Generalized Petersen Graphs and Lollipop Graphs for Some Cases”, Srinakharinwirot Science Journal, vol. 33, no. 2, pp. 195-212, 2017.

2022-09-27

## How to Cite

[1]
. A. Busakorn, R. Boonklurb, and S. . Promvichitkul, “Combination labelings of graphs related to several cycles and paths”, Proyecciones (Antofagasta, On line), vol. 41, no. 5, pp. 1153-1172, Sep. 2022.

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