Dominating sets and domination polynomial of k_r-gluingof graphs
Joint Authors
Source
Dirasat Tarbawiya : Journal of Educational Studies
Issue
Vol. 14, Issue 56 (sup) (31 Dec. 2021), pp.19-28, 10 p.
Publisher
The Ministry of Education The Educational Studies and Research Center
Publication Date
2021-12-31
Country of Publication
Iraq
No. of Pages
10
Main Subjects
Abstract EN
Let G=(V, E) be a simple graph.
Aset D⊆V is a dominating set of G, if every vertex in V-D is adjacent to at least one vertex in D.
Let G be k_r-gluing of G_1 and G_2and denote by C[G_1 ∪_r G_2] the family of all k_r-gluing of G_1and G_2.
Let K_t be complete graph with order t and K_m be complete graph with order m and let G be k_r-gluing of K_t and K_m with order n=m+t-r.
Let G_n^i be the family of dominating sets of G_n with cardinality i, and let d(G_n, i)=|G_n^i |.
In this paper, we construct G_n^i, and obtain a recursive formula for d(G_n, i).
Using this recursive formula, we consider the polynomial D(G_n, x)=∑_(i=1)^n▒〖d(G_n, i)x_i 〗, which we call domination polynomial of k_r-gluing of graphs and obtain some properties of this polynomial.
American Psychological Association (APA)
Kahat, Sahib Sh.& Khalaf, A. M.. 2021. Dominating sets and domination polynomial of k_r-gluingof graphs. Dirasat Tarbawiya : Journal of Educational Studies،Vol. 14, no. 56 (sup), pp.19-28.
https://search.emarefa.net/detail/BIM-1311627
Modern Language Association (MLA)
Kahat, Sahib Sh.& Khalaf, A. M.. Dominating sets and domination polynomial of k_r-gluingof graphs. Dirasat Tarbawiya : Journal of Educational Studies Vol. 14, no. 56 (Supplement) (2021), pp.19-28.
https://search.emarefa.net/detail/BIM-1311627
American Medical Association (AMA)
Kahat, Sahib Sh.& Khalaf, A. M.. Dominating sets and domination polynomial of k_r-gluingof graphs. Dirasat Tarbawiya : Journal of Educational Studies. 2021. Vol. 14, no. 56 (sup), pp.19-28.
https://search.emarefa.net/detail/BIM-1311627
Data Type
Journal Articles
Language
English
Notes
-
Record ID
BIM-1311627