IPM Calendar 
Saturday 12 October 2024   Today  
Events for day: Wednesday 02 October 2024    
           14:00 - 15:00     Combinatorics and Computing Weekly Seminar
Orthogonal 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 ...