E-resources
Peer reviewed
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WANG, SAI; WONG, DEIN; TIAN, FENGLEI
Bulletin of the Australian Mathematical Society, 04/2021, Volume: 103, Issue: 2Journal Article
Abstract An undirected graph $G$ is determined by its $T$ -gain spectrum (DTS) if every $T$ -gain graph cospectral to $G$ is switching equivalent to $G$ . We show that the complete graph $K_{n}$ and the graph $K_{n}-e$ obtained by deleting an edge from $K_{n}$ are DTS, the star $K_{1,n}$ is DTS if and only if $n\leq 2$ , and an odd path $P_{2m+1}$ is not DTS if $m\geq 2$ . We give an operation for constructing cospectral $T$ -gain graphs and apply it to show that a tree of arbitrary order (at least $5$ ) is not DTS.
