Classification Graphs with Large Strong Roman Domination Number

G. Suresh Singh; Narges Mohsenitonekaboni

doi:https://doi.org/10.14445/22315373/IJMTT-V49P531

International Journal of Mathematics Trends and Technology

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Volume 49 | Number 4 | Year 2017 | Article Id. IJMTT-V49P531 | DOI : https://doi.org/10.14445/22315373/IJMTT-V49P531

Classification Graphs with Large Strong Roman Domination Number

G. Suresh Singh, Narges Mohsenitonekaboni

Citation :

G. Suresh Singh, Narges Mohsenitonekaboni, "Classification Graphs with Large Strong Roman Domination Number," International Journal of Mathematics Trends and Technology (IJMTT), vol. 49, no. 4, pp. 210-219, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V49P531

Abstract

the function f :V  0 , 1 , 2 , 3 is named a Strong Roman dominating function on a graph G whenever for each vertex u with f  u   0 there exists an adjacent vertex v to u such that f  v   3 . Also for each vertex u with f  u   1 there should be at least one adjacent vertex v to u weight 2 . The weight of an SRDF is denoted as f V  and        u V f V f u . Strong Roman domination number of a graph G which we denoted by  G  SR  is minimum weight of an SRDF on G . In this paper, we characterize all connected graphs of order n with Strong Roman domination numbers 2 n  2 , 2 n  3 , 2 n  4 and 2 n  5 . Also we present the properties of connected graph of order n with Strong Roman domination number 2 n  6 .

Keywords

Strong Roman domination number, Strong Roman domination function.

References

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