arXiv (OAI Expanded)
open access
A proof of the resistance diameter conjecture for line graphs
We prove the conjecture of Xu, Li, Hua, and Pan that the resistance diameter does not increase under the line-graph operation. For every finite connected simple graph $G$ with at least one edge, we establish $D_r(L(G))\le D_r(G)$, with equality if and only if $G$ is a cycle or $K_4$. The proof combi
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