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Signed bicyclic graphs with minimal index | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 17، دوره 8، شماره 1، خرداد 2023، صفحه 207-241 اصل مقاله (720.96 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27346.1241 | ||
| نویسندگان | ||
| Maurizio Brunetti* ؛ Adriana Ciampella | ||
| Dipartimento di Matematica e Applicazioni R. Caccioppoli. Universita' di Napoli Federico II | ||
| چکیده | ||
| The index $\lambda_1(\Gamma)$ of a signed graph $\Gamma=(G,\sigma)$ is just the largest eigenvalue of its adjacency matrix. For any $n \geqslant 4$ we identify the signed graphs achieving the minimum index in the class of signed bicyclic graphs with $n$ vertices. Apart from the $n=4$ case, such graphs are obtained by considering a starlike tree with four branches of suitable length (i.e.\ four distinct paths joined at their end vertex $u$) with two additional negative independent edges pairwise joining the four vertices adjacent to $u$. As a by-product, all signed bicyclic graphs containing a theta-graph and whose index is less than $2$ are detected. | ||
| کلیدواژه‌ها | ||
| Signed Graph؛ Bicyclic Graph؛ Index؛ Extremal Graph Theory | ||
| مراجع | ||
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