On balance and consistency preserving 2-path signed graphs
| Main Authors: | Chettri, Kshittiz; Department of Mathematics, Nar Bahadur Bhandari Govt. College, Tadong, Sikkim, India, Deb, Biswajit; Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Sikkim, India., Gautam, Anjan; Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Sikkim, India, 737132 |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2023
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1566 https://www.ejgta.org/index.php/ejgta/article/view/1566/pdf_277 |
Daftar Isi:
- Let Σ = (G, σ) be a balanced and canonically consistent signed graph. The 2-path signed graph Σ#Σ = (G2, σ′) of Σ has the underlying graph as G2 and the sign σ′(uv) of an edge uv in it is −1 whenever in each uv-path of length 2 in Σ all edges are negative; otherwise σ′(uv) is 1. Here, G2 is the graph obtained from G by adding an edge between u and v if there is a path of length 2 between them. In this article, we have investigated balancedness and canonically consistency of 2-path signed graphs Σ#Σ of a balanced and canonically consistent signed graph Σ. The problem has been resolved completely for cycles, star graphs and trees.