Mycielskian of Signed Graphs
Albin Mathew, Germina K. A.
TL;DR
This paper introduces the concept of the Mycielskian for signed graphs, exploring its properties related to balance, switching, and chromatic number, and analyzing associated matrices.
Contribution
It defines the Mycielskian for signed graphs and investigates its properties, including conditions for balance and relationships with chromatic numbers.
Findings
Condition for balance preservation in Mycielskian
Relation between chromatic numbers of original and Mycielskian graphs
Structural analysis of matrices related to the Mycielskian
Abstract
In this paper, we define the Mycielskian of a signed graph and discuss the properties of balance and switching in the Mycielskian of a given signed graph. We provide a condition for ensuring the Mycielskian of a balanced signed graph remains balanced, leading to the construction of a balanced Mycielskian. We establish a relation between the chromatic numbers of a signed graph and its Mycielskian. We also study the structure of different matrices related to the Mycielskian of a signed graph.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Graph theory and applications