a-Are-there-any-graphs-with-5-vertices-which-have-vertices-of-degrees-1-2-3-4-and-5-

Question Number 133318 by bramlexs22 last updated on 21/Feb/21

$$\left(\mathrm{a}\right)\:\mathrm{Are}\:\mathrm{there}\:\mathrm{any}\:\mathrm{graphs}\:\mathrm{with}\:\mathrm{5} \\ $$$$\mathrm{vertices}\:\mathrm{which}\:\mathrm{have}\:\mathrm{vertices}\:\mathrm{of}\: \\ $$$$\mathrm{degrees}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{and}\:\mathrm{5}?\: \\ $$

Answered by EDWIN88 last updated on 21/Feb/21

$$\mathrm{No};\:\mathrm{if}\:\mathrm{a}\:\mathrm{graph}\:\mathrm{has}\:\mathrm{n}\:\mathrm{vertices}\:\mathrm{it}\:\mathrm{can}\:\mathrm{have}\:\mathrm{no}\: \\ $$$$\mathrm{vertex}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{bigger}\:\mathrm{than}\:\mathrm{n}−\mathrm{1}\: \\ $$

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