Abstract
In this note, we establish a theorem concerning the common polynomials of the cospectral classes of signed graphs on a given graph in which all the cycles are of the same length and pass through a single point. This theorem is observed to give a doubly infinite class of graphs serving as counterexamples to a recent conjecture on a certain number associated with a cospectral class of unbalanced signed graphs on a given graph.
This work was done when the author was at Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad.
The research partially supported by Department of Atomic Energy, Bombay.
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© 1981 Springer-Verlag
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Gill, M.K. (1981). A note concerning Acharya’s conjecture on a spectral measure of structural balance in a social system. In: Rao, S.B. (eds) Combinatorics and Graph Theory. Lecture Notes in Mathematics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092269
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DOI: https://doi.org/10.1007/BFb0092269
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