Saturday 12 October 2024 |

Events for day: Wednesday 02 October 2024 |

14:00 - 15:00 Combinatorics and Computing Weekly SeminarOrthogonal signatures of graphs School MATHEMATICS ?A signed graph is a pair $G_{sigma}=(G?, sigma)$?, ?where $G$ is a simple graph and $sigma$?, ?called the signature?, ?is a function which assigns 1 or $-1$ to each edge of $G$?. ?We call $sigma$ as an it orthogonal signature of $G$ if? $A(G_{sigma})^2=D$?, ?where $A(G_{sigma})$ is the signed adjacency matrix of $G_{sigma}$ and $D$ is the diagonal matrix with vertex degrees on the diagonal?. ?We have shown that if $G$? has an orthogonal signature?, ?then $G$ should be regular?. ?Graphs with orthogonal signature were crucial in the proof of sensitivity conjecture by Huang in 2019?. ?Hunag used an orthogo ... |