Some properties on the lexicographic product of graphs obtained by monogenic semigroups
Küçük Resim Yok
Tarih
2013
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
SPRINGER INTERNATIONAL PUBLISHING AG
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In (Das et al. in J. Inequal. Appl. 2013:44, 2013), a new graph Gamma (S-M) on monogenic semigroups S-M (with zero) having elements {0, x, x(2), x(3),..., x(n)} was recently defined. The vertices are the non-zero elements x, x(2), x(3),..., x(n) and, for 1 <= i, j <= n, any two distinct vertices x(i) and x(j) are adjacent if x(i)x(j) = 0 in S-M. As a continuing study, in an unpublished work, some well-known indices (first Zagreb index, second Zagreb index, Randic index, geometric-arithmetic index, atom-bond connectivity index, Wiener index, Harary index, first and second Zagreb eccentricity indices, eccentric connectivity index, the degree distance) over Gamma (S-M) were investigated by the same authors of this paper. In the light of the above references, our main aim in this paper is to extend these studies to the lexicographic product over Gamma (S-M). In detail, we investigate the diameter, radius, girth, maximum and minimum degree, chromatic number, clique number and domination number for the lexicographic product of any two (not necessarily different) graphs Gamma (S-M(1)) and Gamma (S-M(2)).
Açıklama
Anahtar Kelimeler
monogenic semigroup, lexicographic product, clique number, chromatic number, independence number, domination number
Kaynak
JOURNAL OF INEQUALITIES AND APPLICATIONS
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
