# zbMATH — the first resource for mathematics

Locally $$C^ k_ n$$ graphs. (English) Zbl 0842.05075
Summary: We completely classify the graphs all of whose neighbourhoods of vertices are isomorphic to $$C^k_n$$ $$(2\leq k< n)$$, where $$C^k_n$$ is the $$k$$th power of the cycle $$C_n$$ of length $$n$$.

##### MSC:
 05C75 Structural characterization of families of graphs 05C38 Paths and cycles
##### Keywords:
local characterization; neighbourhoods; cycle
Full Text: