ALGEBRAIC STRUCTURE OF GRAPH OPERATIONS IN TERMS OF DEGREE SEQUENCES

Mishra V. N., Delen S., CANGÜL İ. N.

INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, cilt.16, sa.6, ss.809-821, 2018 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 6
  • Basım Tarihi: 2018
  • Dergi Adı: INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.809-821
  • Anahtar Kelimeler: graph, degree sequence, join, Corona product, graph operation
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this paper, by means of the degree sequences (DS) of graphs and some graph theoretical and combinatorial methods, we determine the algebraic structure of the set of simple connected graphs according to two graph operations, namely join and Corona product. We shall conclude that in the case of join product, the set of graphs forms an abelian monoid whereas in the case of Corona product, this set is not even associative, it only satisfies two conditions, closeness and identity element. We also give a result on distributive law related to these two operations.