Revista de la
Unión Matemática Argentina
Signed graphs with totally disconnected star complements
Zoran Stanić
Volume 62, no. 1 (2021), pp. 95–104

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We are interested in a signed graph $\dot{G}$ which admits a decomposition into a totally disconnected (i.e., without edges) star complement and a signed graph $\dot{S}$ induced by the star set. In this study we derive certain properties of $\dot{G}$; for example, we prove that the number of (distinct) eigenvalues of $\dot{S}$ does not exceed the number of those of $\dot{G}$. Some particular cases are also considered.