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Q-G-V-E-is-a-graph-such-that-V-G-20-G-8-G-3-find-the-value-of-q-max-q-min-q-E-G-




Question Number 185890 by mnjuly1970 last updated on 29/Jan/23
    Q:     G( V , E )  is a graph , such that              ∣  V (G )∣ = 20 ,  Δ ( G )= 8 ,  δ (G )=3             find  the value of  ,  q_( max)  − q_( min)  = ?              q = ∣ E (G )∣
$$ \\ $$$$\:\:{Q}:\:\:\:\:\:{G}\left(\:{V}\:,\:{E}\:\right)\:\:{is}\:{a}\:{graph}\:,\:{such}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mid\:\:{V}\:\left({G}\:\right)\mid\:=\:\mathrm{20}\:,\:\:\Delta\:\left(\:{G}\:\right)=\:\mathrm{8}\:,\:\:\delta\:\left({G}\:\right)=\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:\:,\:\:{q}_{\:{max}} \:−\:{q}_{\:{min}} \:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{q}\:=\:\mid\:{E}\:\left({G}\:\right)\mid\:\: \\ $$
Answered by MrGaster last updated on 02/Nov/24
q_(mam) −q_(mim) =(1/2)(Σ_(v∈V(G)) Δ(G)−Σ_(v∈V(G)) δ(G))  =(1/2)(20∙8−20∙3)  =(1/2)(160−60)  =(1/2)∙100  =50
$${q}_{{mam}} −{q}_{{mim}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\underset{{v}\in{V}\left({G}\right)} {\sum}\Delta\left({G}\right)−\underset{{v}\in{V}\left({G}\right)} {\sum}\delta\left({G}\right)\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{20}\centerdot\mathrm{8}−\mathrm{20}\centerdot\mathrm{3}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{160}−\mathrm{60}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\centerdot\mathrm{100} \\ $$$$=\mathrm{50} \\ $$

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