کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423526 | 1342400 | 2012 | 8 صفحه PDF | دانلود رایگان |

The subdivision graph S(Σ) of a graph Σ is obtained from Σ by 'adding a vertex' in the middle of every edge of Σ. Various symmetry properties of S(Σ) are studied. We prove that, for a connected graph Σ, S(Σ) is locally s-arc transitive if and only if Σ is âs+12â-arc transitive. The diameter of S(Σ) is 2d+δ, where Σ has diameter d and 0⩽δ⩽2, and local s-distance transitivity of S(Σ) is defined for 1⩽s⩽2d+δ. In the general case where s⩽2dâ1 we prove that S(Σ) is locally s-distance transitive if and only if Σ is âs+12â-arc transitive. For the remaining values of s, namely 2d⩽s⩽2d+δ, we classify the graphs Σ for which S(Σ) is locally s-distance transitive in the cases, s⩽5 and s⩾15+δ. The cases max{2d,6}⩽s⩽min{2d+δ,14+δ} remain open.
Journal: Discrete Mathematics - Volume 312, Issue 1, 6 January 2012, Pages 86-93