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Yıl 2019, Cilt: 9 Sayı: 3, 638 - 645, 01.09.2019

Öz

Kaynakça

  • B. D. Acharya, (2012). Set-valuations of signed digraphs, J. Combin. Inform. System Sci., 37(2- )(2012), 145–167.
  • J Akiyama, D. Avis, V. Cha´vtal and H. Era, (1981). Balancing signed graphs, Discrete App. Math., (4), 227–233., DOI: 10.1016/0166-218X(81)90001-9.
  • P. K. Ashraf, K. A. Germina and N. K. Sudev, A study on set-valuations of signed graphs, Southeast Asian Bull. Math., to appear. J. A. Gallian, (2016). A dynamic survey of graph labeling, Electron. J. Combin., (#DS-6).
  • K. A. Germina and S. Hameed, (2010). On signed paths, signed cycles and their energies, Appl. Math. Sci., 4(70) 3455–3466.
  • K. A. Germina and N. K. Sudev, (2013). On weakly uniform integer additive set-indexers of graphs
  • Int. Math. Forum, 8(37), 1827–1834. DOI: 10.12988/imf.2013.310188.
  • F. Harary, (2001) Graph theory, Narosa Publ. House., New Delhi.
  • F. Harary, (1953). On the notion of balance of a signed graph, The Michigan Math. J., 2(2), 143–146.
  • M. B. Nathanson, (1996). Additive number theory, inverse problems and geometry of sumsets, Springer, New York.
  • N. K. Sudev and K. A. Germina, (2014). On integer additive set-indexers of graphs, Int. J. Math. Sci. Engg. Appl., 8(2)(2014), 11–22.
  • N. K. Sudev and K. A. Germina, A study on arithmetic integer additive set-indexers of graphs, J. Inform. Math. Sci., to appear. N. K. Sudev and K. A. Germina, (2015) On certain types of arithmetic integer additive set-indexers of graphs, Discrete Math. Algorithms Appl., 7(1),1–15., DOI: 10.1142/S1793830915500251.
  • N. K. Sudev and K. A. Germina, (2015). A study on integer additive set-valuation of signed graphs
  • Carpathian Math. Publ., 7(2), 236–246., DOI:10.15330/cmp.7.2.236-246.
  • D. B. West, (2001). Introduction to graph theory, Pearson Education Inc., Delhi.
  • T. Zaslavsky, (1982). Signed graphs, Discrete Appl. Math., 4(1),47–74., DOI: 10.1016/0166- X(82)90033-6.

SOME NEW RESULTS ON INTEGER ADDITIVE SET-VALUED SIGNED GRAPHS

Yıl 2019, Cilt: 9 Sayı: 3, 638 - 645, 01.09.2019

Öz

Let X denotes a set of non-negative integers and P X be its power set. An integer additive set-labeling IASL of a graph G is an injective set-valued function f : V G → P X − {∅} such that the induced function f + : E G → P X − {∅} is defined by f + uv = f u + f v ; ∀ uv ∈ E G , where f u + f v is the sumset of f u and f v . An IASL of a signed graph is an IASL of its underlying graph G together with the signature σ defined by σ uv = −1 |f+ uv | ; ∀ uv ∈ E Σ . In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive set-labelings.

Kaynakça

  • B. D. Acharya, (2012). Set-valuations of signed digraphs, J. Combin. Inform. System Sci., 37(2- )(2012), 145–167.
  • J Akiyama, D. Avis, V. Cha´vtal and H. Era, (1981). Balancing signed graphs, Discrete App. Math., (4), 227–233., DOI: 10.1016/0166-218X(81)90001-9.
  • P. K. Ashraf, K. A. Germina and N. K. Sudev, A study on set-valuations of signed graphs, Southeast Asian Bull. Math., to appear. J. A. Gallian, (2016). A dynamic survey of graph labeling, Electron. J. Combin., (#DS-6).
  • K. A. Germina and S. Hameed, (2010). On signed paths, signed cycles and their energies, Appl. Math. Sci., 4(70) 3455–3466.
  • K. A. Germina and N. K. Sudev, (2013). On weakly uniform integer additive set-indexers of graphs
  • Int. Math. Forum, 8(37), 1827–1834. DOI: 10.12988/imf.2013.310188.
  • F. Harary, (2001) Graph theory, Narosa Publ. House., New Delhi.
  • F. Harary, (1953). On the notion of balance of a signed graph, The Michigan Math. J., 2(2), 143–146.
  • M. B. Nathanson, (1996). Additive number theory, inverse problems and geometry of sumsets, Springer, New York.
  • N. K. Sudev and K. A. Germina, (2014). On integer additive set-indexers of graphs, Int. J. Math. Sci. Engg. Appl., 8(2)(2014), 11–22.
  • N. K. Sudev and K. A. Germina, A study on arithmetic integer additive set-indexers of graphs, J. Inform. Math. Sci., to appear. N. K. Sudev and K. A. Germina, (2015) On certain types of arithmetic integer additive set-indexers of graphs, Discrete Math. Algorithms Appl., 7(1),1–15., DOI: 10.1142/S1793830915500251.
  • N. K. Sudev and K. A. Germina, (2015). A study on integer additive set-valuation of signed graphs
  • Carpathian Math. Publ., 7(2), 236–246., DOI:10.15330/cmp.7.2.236-246.
  • D. B. West, (2001). Introduction to graph theory, Pearson Education Inc., Delhi.
  • T. Zaslavsky, (1982). Signed graphs, Discrete Appl. Math., 4(1),47–74., DOI: 10.1016/0166- X(82)90033-6.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

N. K. Sudev Bu kişi benim

P. K. Ashraf Bu kişi benim

K. A. Germina Bu kişi benim

Yayımlanma Tarihi 1 Eylül 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 3

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