Characterization of A Graphs with Signed Domination Number One W.R.T Induced Subgraphs Are Totally Disconnected, Path, Cycle and Complete Graph

• Author(s): M. S. Patil
• Paper ID: 1704897
• Page: 650-660
• Published Date: 31-07-2023
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 7 Issue 1 July-2023

Abstract

A two-valued function f defined on the vertices of a graph G=(V, E), ?: ? ? {?1, 1} is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. The weight of a signed dominating function is defined to be (?) = ? ?(?), over all vertices ? ? ?. The signed dominating number of a graph G, denoted by ??(?) ??? ??(?) = min{w(?)}, where f is signed dominating function of G. In this paper, characterize the class of graphs for signed domination number one with respective to induced subgraphs.

Keywords

Signed dominating function, Signed domination number and induced sub graph

Citations

IRE Journals:
M. S. Patil "Characterization of A Graphs with Signed Domination Number One W.R.T Induced Subgraphs Are Totally Disconnected, Path, Cycle and Complete Graph" Iconic Research And Engineering Journals Volume 7 Issue 1 2023 Page 650-660

IEEE:
M. S. Patil "Characterization of A Graphs with Signed Domination Number One W.R.T Induced Subgraphs Are Totally Disconnected, Path, Cycle and Complete Graph" Iconic Research And Engineering Journals, 7(1)