scholarly journals The average domination polynomial of graphs is unimodal

2021 ◽  
Vol 7 ◽  
pp. 86-89
Keyword(s):  
Domination Polynomial

Hop domination polynomial of graphs

2019 ◽  
Vol 23 (4) ◽  
pp. 825-840 ◽  
Author(s):  
D. A. Mojdeh ◽  
A. S. Emadi
Keyword(s):  
Domination Polynomial

scholarly journals On the Uphill Domination Polynomial of Graphs

2020 ◽  
Vol 08 (06) ◽  
pp. 1168-1179
Author(s):  
Thekra Alsalomy ◽  
Anwar Saleh ◽  
Najat Muthana ◽  
Wafa Al Shammakh
Keyword(s):  
Domination Polynomial

scholarly journals Perfect dominating sets and perfect domination polynomial of a star graph

2020 ◽  
Vol 8 (4) ◽  
pp. 1751-1755
Author(s):  
Paul Hawkins P. ◽  
Anto A.M. ◽  
Shyla Isac Mary T.
Keyword(s):  
Star Graph ◽  
Dominating Sets ◽  
Domination Polynomial

Strong nonsplit dominating sets and strong nonsplit domination polynomial of complement of paths

2020 ◽  
Vol 12 (06) ◽  
pp. 2050082
Author(s):  
D. Kiruba Packiarani ◽  
Y. Therese Sunitha Mary
Keyword(s):  
Domination Number ◽  
Recursive Formula ◽  
Simple Graph ◽  
Dominating Sets ◽  
The Family ◽  
Domination Polynomial

Let [Formula: see text] be a simple graph of order [Formula: see text]. The strong nonsplit domination polynomial of a graph [Formula: see text] is [Formula: see text] where [Formula: see text] is the number of strong nonsplit dominating sets of [Formula: see text] of size [Formula: see text] and [Formula: see text] is the strong nonsplit domination number of [Formula: see text]. Let [Formula: see text] be the family of strong nonsplit dominating sets of a complement of a path [Formula: see text] ([Formula: see text]) with cardinality [Formula: see text], and let [Formula: see text]. In this paper, we construct [Formula: see text], the recursive formula for [Formula: see text] and [Formula: see text], the strong nonsplit domination polynomial of [Formula: see text]. Also, we obtain some properties of the coefficients of this polynomial.

ECCENTRIC DOMINATION POLYNOMIAL OF GRAPHS

2020 ◽  
Vol 9 (4) ◽  
pp. 1729-1739
Author(s):  
A. M. Ismayil ◽  
R. Tejaskumar
Keyword(s):  
Domination Polynomial

The Number of 2-dominating Sets, and 2-domination Polynomial of a Graph

2021 ◽  
Vol 42 (4) ◽  
pp. 751-759
Author(s):  
F. Movahedi ◽  
M. H. Akhbari ◽  
S. Alikhani
Keyword(s):  
Dominating Sets ◽  
Domination Polynomial

scholarly journals Graphs Whose Certain Polynomials Have Few Distinct Roots

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Saeid Alikhani
Keyword(s):  
Simple Graph ◽  
Edge Cover ◽  
Graph Polynomials ◽  
Matching Polynomial ◽  
Domination Polynomial ◽  
Cover Polynomial

Let G=(V,E) be a simple graph. Graph polynomials are a well-developed area useful for analyzing properties of graphs. We consider domination polynomial, matching polynomial, and edge cover polynomial of G. Graphs which their polynomials have few roots can sometimes give surprising information about the structure of the graph. This paper is primarily a survey of graphs whose domination polynomial, matching polynomial, and edge cover polynomial have few distinct roots. In addition, some new unpublished results and questions are concluded.

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