Exclusive graphs: a new link among labelings

Rikio Ichishima, Francesc A. Muntaner-Batle, Akito Oshima


In this paper, we define a strongly felicitous graph to be lower-exclusive, upper-exclusive and exclusive depending on different restrictions for the vertex labels. With these new concepts, we show that the union of finite collection of strongly felicitous graphs, a lower-exclusive one and an upper-exclusive one results in a strongly felicitous graph. We also introduce the concept of decompositional graphs. By means of this, we provide some results involving the cartesian products of exclusive graphs.


exclusive graph; (strongly) felicitous graph; decompositional

Full Text:



G. Chartrand and L. Lesniak, Graphs & Digraphs, second edition. Wadsworth & Brooks/Cole Advanced Books and Software, Monterey (1986).

R. M. Figueroa-Centeno and R. Ichishima, The n-dimensional cube is felicitous, Bull. Inst. Combin. Appl., 41 (2004) 47--50.

R. Figueroa-Centeno, R. Ichishima, and F. Muntaner-Batle, Magical coronations of graphs, Australas. J. Combin., 26 (2002) 199--208.

R. M. Figueroa-Centeno, R. Ichishima, and F. A. Muntaner-Batle, Labeling the vertex amalgamation of graphs, Discuss. Math. Graph Theory, 23 (2003) 129--139.

R. Figueroa-Centeno, R. Ichishima, F. Muntaner-Batle and A. Oshima, A magical approach to some labeling conjectures, Discuss. Math. Graph Theory, 31 (2011) 79--113.

J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. (2018) #DS6.

R. L. Graham and N. J. Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Math., 1 (1980) 382--404.

S. W. Golomb, How to number a graph, in Graph Theory and Computing, R. C. Read, ed., Academic Press, New York (1972) 23--37.

R. Ichishima and A. Oshima, On partitional and other related graphs, Math. Comput. Sci., 5 (2011) 41--50.

A. Kotzig, Decomposition of complete graphs into isomorphic cubes, J. Combin. Theory, Series B, 31 (1981) 292--296.

S. M. Lee, E. Schmeichel, and S. C. Shee, On felicitous graphs, Discrete Math., 93 (1991) 201--209.

K. Manickam, M. Marudai, and R. Kala, Some results on felicitous labeling of graphs, J. Combin. Math. Combin. Comput., 81 (2012) 273--279.

A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967) 87--95.

M. A. Seoud and E. A. Elsahawi, On almost graceful, felicitous and elegant graphs, J. Egyptian Math. Soc., 7 (1999) 137--149.

V. Yegnanarayanan, On some additive analogues of graceful theme: cycle related graphs, Southeast Asian Bull. Math., 23 (1999) 1--17.

DOI: http://dx.doi.org/10.19184/ijc.2019.3.1.1


  • There are currently no refbacks.

ISSN: 2541-2205

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View IJC Stats