Product Signed Domination in Graphs

T M Velammal, A Nagarajan, K Palani


Let  be a simple graph. The closed neighborhood of , denoted by , is the set . A function  is a product signed dominating function, if for every vertex where . The weight of , denoted by , is the sum of the function values of all the vertices in . . The product signed domination number of  is the minimum positive weight of a product signed dominating function. In this paper, we establish bounds on the product signed domination number and estimate product signed domination number for some standard graphs


graphs, product signed dominating function, product signed domination number

Full Text:



J. Dunbar, S.T. Hedetniemi. Henning, and P.J. Slater (1995), Signed Domination in Graph Theory, In: Graph Theory, Combinatorics and Applications, John Wiley & Sons, New York, 311-322.

Ernest J. Cockayneand Christina M. Mynhardt (1996), On AGeneralisation Of Signed Dominating Funtions Of Graphs,ArsCombinatoria, 43, 235-245.

S.M. Hosseini Moghaddam (2015), New Bounds On The Signed Domination Numbers Of Graphs, Australasian Journal Of Combinatorics, 61(3), 273-280

IzakBroere, Johannes H. Hattingh, Michael A. Henning, and Alice A. McRae (1995), Majority Domiation In Graphs, Discrete Mathematics, 138, 125-135.

Odile Favaron (1996), Signed Domination In Regular Graphs, Discrete Mathematics, 158, 287-293.



  • There are currently no refbacks.

Copyright (c) 2022 T M Velammal, A NAGARAJAN, K Palani

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.