A Study on Signed Domatic Number of a Graph

• Author(s): M. S. Patil
• Paper ID: 1703741
• Page: 279-288
• Published Date: 31-08-2022
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 6 Issue 2 August-2022

Abstract

A two-valued function f defined on the vertices of a graph G = (V, E), f: V -> {?1, 1} is a Signed dominating function, if the sum of its function values over any closed neighborhood is at least one. The weight of a signed dominating function is w (f ) = E f (v), over all vertices v ? V. The signed domination number of a graph G, is denoted by Ys(G), equals the minimum weight of a signed dominating function of G. A set f1, f2, f3, ...., fd of signed dominating functions on G with the property that E fi(x) <= 1 for each x E V (G), is called a signed dominating function i=1 on G. The maximum number of functions in a signed dominating family on G is the signed domatic number of G, denoted by ds(G). In this paper, we prove Ys(G) + ds(G) <= n + 1 and ds(G) + ds(G?) <= n + 1. Further, we characterize the class of extremal class of graphs for which both the bounds attain. And to find the exact value of signed domatic number of a circulant graphs. Throughout this paper, we consider only finite, undirected simple graphs we mean without multiple edges or loops.

Keywords

Signed dominating function, Signed domination number, Signed domatic number, AMS Classification:05C

Citations

IRE Journals:
M. S. Patil "A Study on Signed Domatic Number of a Graph" Iconic Research And Engineering Journals Volume 6 Issue 2 2022 Page 279-288

IEEE:
M. S. Patil "A Study on Signed Domatic Number of a Graph" Iconic Research And Engineering Journals, vol. 6, no. 2, Aug. 2022

APA:
M. S. Patil (2022). A Study on Signed Domatic Number of a Graph. Iconic Research And Engineering Journals, 6(2).

MLA:
M. S. Patil "A Study on Signed Domatic Number of a Graph" Iconic Research And Engineering Journals, vol. 6, no. 2, Aug. 2022.

BibTeX

@article{1703741,
author = {M. S. Patil},
title = {A Study on Signed Domatic Number of a Graph},
journal = {Iconic Research And Engineering Journals},
year = {2022},
volume = {6},
number = {2},
pages = {279-288},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1703741.pdf},
abstract = {A two-valued function f defined on the vertices of a graph G = (V, E), f: V -> {?1, 1} is a Signed dominating function, if the sum of its function values over any closed neighborhood is at least one. The weight of a signed dominating function is w (f ) = E f (v), over all vertices v ? V. The signed domination number of a graph G, is denoted by Ys(G), equals the minimum weight of a signed dominating function of G. A set f1, f2, f3, ...., fd of signed dominating functions on G with the property that E fi(x) <= 1 for each x E V (G), is called a signed dominating function i=1 on G. The maximum number of functions in a signed dominating family on G is the signed domatic number of G, denoted by ds(G). In this paper, we prove Ys(G) + ds(G) <= n + 1 and ds(G) + ds(G?) <= n + 1. Further, we characterize the class of extremal class of graphs for which both the bounds attain. And to find the exact value of signed domatic number of a circulant graphs. Throughout this paper, we consider only finite, undirected simple graphs we mean without multiple edges or loops.},
keywords = {Signed dominating function, Signed domination number, Signed domatic number, AMS Classification:05C},
month = {August}
}