Locally snake-like graphs. (English) Zbl 0641.05031

A snake is a connected graph in which exactly two vertices have degree 1 and all others have degree 2. A graph with the property that the neighborhood graph of each vertex is a snake the said to be locally snake-like. Only finite, planar and 3-connected locally snake-like graphs are considered here. Such graphs are characterized and the largest size of such graphs of order n is determined.
Reviewer: R.C.Entringer


05C38 Paths and cycles
05C35 Extremal problems in graph theory
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[1] BLASS A., HARARY F., MILLER Z.: Which trees are link graphs?. J. Comb. Theory (B) 29, 1980, 277-292. · Zbl 0448.05028
[2] CHARTRAND G. PIPPERT G.: Locally connected graphs. Časop. pěst. mat. 99, 1974, 158-163. · Zbl 0278.05113
[3] CLARK L.: Hamiltonian properties of connected, locally connected graphs. Congr. Num. 32, 1981, 199-204. · Zbl 0495.05041
[4] HELL P.: Graphs with given neighbourhoods I. Colloq. Int. CNRS Orsay, 1976, 219-223.
[5] SEDLÁČEK J.: Lokální vlastnosti grafů. (Local properties of graphs.) Časop. p\?st. mat. 106, 1981, 290-298
[6] SEDLÁČEK J.: On local properties of finite graphs. Graph Theory, Łagów 1981. Springer-Verlag Berlin-Heidelberg-New York Tokyo 1983. · Zbl 0531.05056
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