Signed Domination in Signed Graphs

By : H.B. Walikar, Satish V. Motammanavar, B. D. Acharya

Page No: 107-128

Abstract Let S = (V,E, ?) be a signed graph, a function f : V ? {?1, +1} is a signed domination function (SDF) of S if f(N[v]) ? 1 where f(N[v]) = f (v)+ ?(uv) f(u), for every v ? V. Every graph can be viewed as a signed graph in which every edge is positive and every graph admits a signed dominating function but it is not true in case of heterogeneous signed graphs (i.e, signed graph possessing at least one negative edge). In this paper we characterize some classes of signed graphs which admit the signed domination function and we have also shown that signed graph can be embedded as an induced subgraph of a signed graph that admits an SDF

Authors :
H.B. Walikar : Former Professor and Head Department of Computer Science, Karnatak University Dharwad, Karnataka, India.
Satish V. Motammanavar : Department of Mathematics, R. V. College of Engineering, Bangalore, Karnataka, India.
B. D. Acharya : Ex-Director PIMSci Karnatak University, Dharwad, Karnataka, India.