Affiliation:
1. Department of Mathematics , CHRIST (Deemed to be University) , Bangalore - , Karnataka , India .
Abstract
AbstractA signed graph is a graph in which positive or negative signs are assigned to its edges. We consider equitable colouring and Hamiltonian colouring to obtain induced signed graphs. An equitable colour-induced signed graph is a signed graph constructed from a given graph in which each edge uv receives a sign (−1)|c(v)−c(u)|,where c is an equitable colouring of vertex v. A Hamiltonian colour-induced signed graph is a signed graph obtained from a graph G in which for each edge e = uv, the signature function σ(uv)=(−1)|c(v)−c(u)|, gives a sign such that, |c(u)− c(v)| ≥ n − 1 − D(u, v) where c is a function that assigns a colour to each vertex satisfying the given condition. This paper discusses the properties and characteristics of signed graphs induced by the equitable and Hamiltonian colouring of graphs.
Reference14 articles.
1. [1] A. Aniyan, S. Naduvath, Induced signed graph of some classes of graphs, Proc. Jangjeon Math. Soc., 23(2020), pp. 283-291, doi: 10.17777/pjms2020.23.2.283. ⇒340
2. [2] A. Aniyan, S. Naduvath, On degree product induced signed graphs of graphs, AIP Conference Proceedings, 1(2020), pp. 030018, doi:10.1063/5.0019097 ⇒34010.1063/5.0019097
3. [3] G. Chartrand, L. Nebesk‘y, P. Zhang, Hamiltonian colorings of graphs, Discrete Appl. Math., 146(2005), pp. 257-272, doi:10.1016/j.dam.2004.08.007 ⇒34010.1016/j.dam.2004.08.007
4. [4] Y. Chen, J.L. Gross, T. Mansour, Total embedding distributions of circular ladders, J. Graph Theory, 74(2013), pp. 32-57, doi:10.1016/j.disc.2011.07.020 ⇒34310.1016/j.disc.2011.07.020
5. [5] F. Harary, On the notion of balance of a signed graph, Michigan Math. J., 2(1953), pp. 143-146, doi: 10.1307/mmj/1028989917 ⇒339, 34110.1307/mmj/1028989917