ON CONNECTED TOTAL DOMINATION POLYNOMIAL OF SOME LEXICOGRAPHIC PRODUCT GRAPHS

2021 ◽  
Vol 27 (1) ◽  
pp. 147-155
Author(s):  
Giovannie M. Entero ◽  
Ariel C. Pedrano
Keyword(s):  
Total Domination ◽  
Lexicographic Product ◽  
Product Graphs ◽  
Domination Polynomial ◽  
Lexicographic Product Graphs

scholarly journals Double domination in lexicographic product graphs

2020 ◽  
Vol 284 ◽  
pp. 290-300 ◽  
Author(s):  
Abel Cabrera Martínez ◽  
Suitberto Cabrera García ◽  
J.A. Rodríguez-Velázquez
Keyword(s):  
Lexicographic Product ◽  
Product Graphs ◽  
Double Domination ◽  
Lexicographic Product Graphs

Path 3-(edge-)connectivity of lexicographic product graphs

2020 ◽  
Vol 282 ◽  
pp. 152-161
Author(s):  
Tianlong Ma ◽  
Jinling Wang ◽  
Mingzu Zhang ◽  
Xiaodong Liang
Keyword(s):  
Lexicographic Product ◽  
Edge Connectivity ◽  
Product Graphs ◽  
Lexicographic Product Graphs

scholarly journals On the weak Roman domination number of lexicographic product graphs

2019 ◽  
Vol 263 ◽  
pp. 257-270 ◽  
Author(s):  
Magdalena Valveny ◽  
Hebert Pérez-Rosés ◽  
Juan A. Rodríguez-Velázquez
Keyword(s):  
Domination Number ◽  
Lexicographic Product ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Product Graphs ◽  
Lexicographic Product Graphs

scholarly journals On independent position sets in graphs

2021 ◽  
Vol 40 (2) ◽  
pp. 385-398
Author(s):  
Elias John Thomas ◽  
Ullas Chandran S. V.
Keyword(s):  
Independent Set ◽  
Maximum Size ◽  
General Relationship ◽  
Lexicographic Product ◽  
Graph Invariants ◽  
General Properties ◽  
Product Graphs ◽  
Related Graph ◽  
Corona Product ◽  
Lexicographic Product Graphs

An independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, we introduce and study the independent position number of a graph. Certain general properties of these concepts are discussed. Graphs of order n having the independent position number 1 or n − 1 are characterized. Bounds for the independent position number of Cartesian and Lexicographic product graphs are determined and the exact value for Corona product graphs are obtained. Finally, some realization results are proved to show that there is no general relationship between independent position sets and other related graph invariants.

scholarly journals Lexicographic product graphs Pm[Pn] are antimagic

2018 ◽  
Vol 15 (3) ◽  
pp. 271-283
Author(s):  
Wenhui Ma ◽  
Guanghua Dong ◽  
Yingyu Lu ◽  
Ning Wang
Keyword(s):  
Lexicographic Product ◽  
Product Graphs ◽  
Lexicographic Product Graphs

Partially composed property of generalized lexicographic product graphs

2017 ◽  
Vol 09 (06) ◽  
pp. 1750079
Author(s):  
Nopparat Pleanmani ◽  
Boyko Gyurov ◽  
Sayan Panma
Keyword(s):  
Lexicographic Product ◽  
Minimum Cardinality ◽  
Product Graphs ◽  
Lexicographic Product Graphs

For a vertex property [Formula: see text] and a graph [Formula: see text], a set [Formula: see text] of vertices of [Formula: see text] is a [Formula: see text]-set of [Formula: see text] if [Formula: see text]. The maximum and minimum cardinality of a [Formula: see text]-set of [Formula: see text] are denoted by [Formula: see text] and [Formula: see text], respectively. If [Formula: see text] is a [Formula: see text]-set such that its cardinality equals [Formula: see text] or [Formula: see text], we say that [Formula: see text] is an [Formula: see text]-set or [Formula: see text]-set of [Formula: see text], respectively. In this paper, we obtain such numbers of generalized lexicographic product graphs in some vertex properties.

scholarly journals From Italian domination in lexicographic product graphs to w-domination in graphs

2021 ◽  
Author(s):  
Abel Cabrera Martinez ◽  
Alejandro Estrada-Moreno ◽  
Juan Alberto Rodriguez-Velazquez
Keyword(s):  
Lexicographic Product ◽  
Product Graphs ◽  
Domination In Graphs ◽  
Lexicographic Product Graphs
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