On singular signed graphs with nullspace spanned by a full vector: signed nut graphs
نویسندگان
چکیده
A signed graph has edge weights drawn from the set $\{+1,-1\}$, and is termed sign-balanced if it equivalent to an unsigned under operation of sign switching; otherwise called sign-unbalanced. nut a one dimensional kernel with corresponding eigenvector that full. In this paper we generalise notion graphs graphs. Orders for which regular exist were determined recently degrees up $11$. By extending definition graphs, find all pairs $(\rho, n)$ $\rho$-regular (sign-balanced or sign-unbalanced) order $n$ exists $\rho \le 11$. We devise construction based on smaller `seed' graph, giving infinite series both sign-unbalanced All orders complete are characterised; they have underlying $K_n$ $n \equiv 1 \pmod 4$. = n - 2$ also cocktail-party $\mathrm{CP}(n)$ even \geq 8$.
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2021
ISSN: ['1234-3099', '2083-5892']
DOI: https://doi.org/10.7151/dmgt.2436