Affiliations: [a] Department of Mathematical Sciences, United ArabEmirates University, Al Ain, United Arab Emirates
| [b] College of Electrical and Mechanical Engineering, (CEME), National University of Sciences and Technology (NUST), Sector H-12, Islamabad, Pakistan
| [c] Department of Mathematics, Riphah Institute ofComputing and Applied Sciences, Riphah International University, Lahore, Pakistan
| [d] Department of Mathematics, School of NaturalSciences (SNS), National University of Sciences and Technology(NUST), Sector H-12, Islamabad, Pakistan
Correspondence:
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Corresponding author. Muhammad Imran, Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, United Arab Emirates. E-mail: [email protected].
Abstract: Chromatic spectrum of a colored graph G is a multiset of eigenvalues of colored adjacency matrix of G. The nullity of a disconnected graph is equal to sum of nullities of its components but we show that this result does not hold for colored graphs. In this paper, we investigate the chromatic spectrum of three different classes of 2-regular bipartite colored graphs. In these classes of graphs, it is proved that the nullity of G is not sum of nullities of components of G. We also highlight some important properties and conjectures to extend this problem to general graphs.
Keywords: Spectrum of graph, nullity of graph, graph coloring
