<abstract xmlns="http://www.w3.org/1999/xhtml">

A 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.
</abstract>

A 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.

Some new results on colour-induced signed graphs

niranjana.sudheer@maths.christuniversity.in

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Some new results on colour-induced signed graphs"}

A 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...

Some new results on colour-induced signed graphs

Published Online: Feb 04, 2023

Page range: 338 - 353

Received: Aug 24, 2022

Accepted: Jan 18, 2023

DOI: https://doi.org/10.2478/ausi-2022-0019

Keywords
Equitable colour-induced signed graphs, Hamiltonian colour-induced signed graphs, balance, clusterability, consistent

© 2022 Niranjana Sudheer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Some new results on colour-induced signed graphs

Published Online: Feb 04, 2023

Page range: 338 - 353

Received: Aug 24, 2022

Accepted: Jan 18, 2023

DOI: https://doi.org/10.2478/ausi-2022-0019

KeywordsEquitable colour-induced signed graphs, Hamiltonian colour-induced signed graphs, balance, clusterability, consistent

© 2022 Niranjana Sudheer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Equitable colour-induced signed graphs, Hamiltonian colour-induced signed graphs, balance, clusterability, consistent