A study on prime arithmetic integer additive set-indexers of graphs.

• Autores: N. K. Sudev, K. A. Germina
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 36, Nº. 2, 2017, págs. 195-208
• Idioma: inglés
• DOI: 10.4067/S0716-09172017000200195
• Enlaces
  • Texto completo
• Resumen

  • Let N₀ be the set of all non-negative integers and P(N₀)be its power set. An integer additive set-indexer (IASI) is defined as an injective function f:V (G) → P(N₀) such that the induced function f⁺: E (G) → P(N₀) defined by f⁺(uv) = f(u) + f(v) is also injective, where N₀ is the set of all non-negative integers. A graph G which admits an IASI is called an IASI graph. An IASI of a graph G is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of G are in arithmetic progressions. In this paper, we discuss about a particular type of arithmetic IASI called prime arithmetic IASI.

• Referencias bibliográficas
  • ACHARYA, B. D. (1990) Arithmetic graphs. EN: J. Graph Theory, 14(3). [s.l.: s.n.], pp. 275-299.
  • ACHARYA, B. D. (2008) Some new perspective on arithmetic graphs in Labeling of Discrete Structures and Applications. New Delhi: Narosa Pub....
  • APOSTOL, T. M. (1989) Introduction to analytic number theory. New York: Springer Verlag.
  • BONDY, J. A. (2008) Graph theory. [s.l.]: Springer.
  • BRANDSTÄDT, A. (1999) Graph classes: A survey. Philadelphia: SIAM.
  • CHARTRAND, G. (2005) Introduction to graph theory. [s.l.]: McGrawHill Inc.
  • DEO, N. (1974) Graph theory with applications to engineering and computer science. Delhi: PHI Learning.
  • GALLIAN, J. A. (2014) A dynamic survey of graph labeling. EN: Electron. J. Combin. (DS-6). [s.l.: s.n.]
  • GERMINA, K. A. (2012) Anandavally, Integer additive set-indexers of a graph: sum square graphs. EN: J. Combin. Inform. System Sci., 37(2-4)....
  • GERMINA, K. A. (2013) On weakly uniform integer additive set-indexers of graphs. EN: Int. Math. Forum., 8(37). [s.l.: s.n.], 1827-1834. DOI:...
  • GROSS, J. ( 1999) Graph theory and its applications. [s.l.]: CRC Press.
  • HARARY, F. (1969) Graph theory. [s.l.]: Addison-Wesley Pub. Co. Inc.
  • JOSHI, K. D. (2003) Applied discrete structures. [s.l]: New Age International.
  • HEGDE, S. M. (1989) Numbered graphs and their applications, Ph.D. Thesis. India: Delhi University.
  • NATHANSON, M. B. (1996) Additive number theory: Inverse problems and geometry of sumsets. [s.l.]: Springer.
  • SUDEV, N. K. (2014) On integer additive set-indexers of graphs. EN: Int. J. Math. Sci.& Engg. Appl., 8(2). [s.l.: s.n.], 11-22.
  • SUDEV, N. K. (2015) Some new results on strong integer additive set-indexers of graphs. EN: Discrete Math. Algorithms Appl., 7(1). [s.l.:...
  • SUDEV, N. K. (20??) A study on arithmetic integer additive set-indexers of graphs. EN: Carpathian Math. Pub., J. Inform. Math. Sci. [s.l.:...
  • SUDEV, N. K. (2015) On certain arithmetic integer additive set-indexers of graphs. EN: Discrete Math. Algorithms Appl., 7(3). (2015), [s.l.:...
  • SUDEV, N. K. (2014) A study on semi-arithmetic integer additive set-indexers of graphs. EN: Int. J. Math. Sci. & Engg. Appl., 8(3). [s.l.:...
  • WEST, D. B. (2001) Introduction to graph theory. [s.l.]: Pearson Edu. Inc.