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- W1664590880 abstract "Let $v$ be a vertex of a graph $G$. By the local complementation of $G$ at $v$ we mean to complement the subgraph induced by the neighbors of $v$. This operator can be generalized as follows. Assume that, each edge of $G$ has a label in the finite field $mathbf{F}_q$. Let $(g_{ij})$ be set of labels ($g_{ij}$ is the label of edge $ij$). We define two types of operators. For the first one, let $v$ be a vertex of $G$ and $ain mathbf{F}_q$, and obtain the graph with labels $g'_{ij}=g_{ij}+ag_{vi}g_{vj}$. For the second, if $0neq bin mathbf{F}_q$ the resulted graph is a graph with labels $g''_{vi}=bg_{vi}$ and $g''_{ij}=g_{ij}$, for $i,j$ unequal to $v$. It is clear that if the field is binary, the operators are just local complementations that we described. The problem of whether two graphs are equivalent under local complementations has been studied, cite{bouchalg}. Here we consider the general case and assuming that $q$ is odd, present the first known efficient algorithm to verify whether two graphs are locally equivalent or not." @default.
- W1664590880 created "2016-06-24" @default.
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- W1664590880 date "2007-02-09" @default.
- W1664590880 modified "2023-09-27" @default.
- W1664590880 title "An Efficient Algorithm to Recognize Locally Equivalent Graphs in Non-Binary Case" @default.
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