TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS

Alikhani, S.; Jafari, N.

doi:10.22044/jas.2018.1096

TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS

Document Type : Original Manuscript

Authors

S. Alikhani ¹
N. Jafari ²

¹ Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.

² Department of Mathematics, Yazd University, 89195-741 Yazd, Iran.

10.22044/jas.2018.1096

Abstract

Let

G = (V, E)

be a simple graph of order

n

. The total dominating set is a subset

D

V

that every vertex of

V

is adjacent to some vertices of

D

. The total domination number of

G

is equal to minimum cardinality of total dominating set in

G

and denoted by

γ_{t} (G)

. The total domination polynomial of

G

is the polynomial

D_{t} (G, x) = \sum d_{t} (G, i)

, where

d_{t} (G, i)

is the number of total dominating sets of

G

of size

i

. Let

G

be a connected graph constructed from pairwise disjoint connected graphs

G_{1}, \dots, G_{k}

by selecting a vertex of

G_{1}

, a vertex of

G_{2}

, and identify these two
vertices. Then continue in this manner inductively. We say that

G

is obtained by point-attaching from

G_{1}, \dots, G_{k}

and that

G_{i}

's are the primary subgraphs of

G

.
In this paper, we consider some particular cases of these graphs that most of them are of importance in chemistry and study their total domination polynomials.

Keywords

TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS

Volume 5, Issue 2
January 2018
Pages 127-138

Files

Share

How to cite

Statistics

TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS

Volume 5, Issue 2January 2018Pages 127-138

Files

Share

How to cite

Statistics

Volume 5, Issue 2
January 2018
Pages 127-138