ROMAN AND INVERSE ROMAN DOMINATION IN NETWORK OF TRIANGLES

In graph G (V, E), a function f: V [right arrow] {0,1 2} is said to be a Roman Dominating Function (RDF). If Au [member of] V, f(u) = 0 is adjacent to at least one vertex v [member of] V such that f(v) = 2. The weight of f is given by [Please download the PDF to view the mathematical expression]. Th...

Full description

Saved in:
Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 2; p. 546
Main Authors Kumar, M. K, Dhanasekar, N, Prasath, G. M. A, Giri, R
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.04.2023
Elman Hasanoglu
Subjects
Apexes
Graph theory
Graphs
Mathematical functions
Minimum weight
Roman civilization
Social networks
Iran
Oman
Online AccessGet full text
ISSN2146-1147
2146-1147

Cover

More Information
Summary:In graph G (V, E), a function f: V [right arrow] {0,1 2} is said to be a Roman Dominating Function (RDF). If Au [member of] V, f(u) = 0 is adjacent to at least one vertex v [member of] V such that f(v) = 2. The weight of f is given by [Please download the PDF to view the mathematical expression]. The Roman Domination Number (RDN) denoted by [gama]r(G) is the minimum weight among all RDF in G. If V - D contains a RDF [f.sup.1]: V [right arrow] {0,1, 2}, where D is the set of vertices v, f(v) > 0, then [f.sup.1] is called Inverse Roman Dominating Function (IRDF) on a graph G with respect to the RDF f. The Inverse Roman Domination Number (IRDN) denoted by [Please download the PDF to view the mathematical expression](G) is the minimum weight among all IRDF in G. In this paper we find RDN and IRDN of few triangulations graphs. Keywords: Domination Number, Roman Domination Number, Inverse Domination Number. AMS Subject Classification: 05C69, 94C15, 68R10.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2146-1147
2146-1147