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arxiv: 1012.3942 · v1 · pith:PZNUAJBHnew · submitted 2010-12-17 · 🧮 math.CO

Distance-balanced closure of some graphs

classification 🧮 math.CO
keywords distance-balancedclosuredeltagraphclosuresdefinefindgraphs
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In this paper we prove that any distance-balanced graph $G$ with $\Delta(G)\geq |V(G)|-3$ is regular. Also we define notion of distance-balanced closure of a graph and we find distance-balanced closures of trees $T$ with $\Delta(T)\geq |V(T)|-3$.

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