Question

Prove that the vertices of G consists of k carbon atoms and m hydrogen atoms then G has a total degree of 4k+m

Answer 1

@Zarkon can u help me?

Answer 2

@KingGeorge plleeassseee heeelllpppp me

Answer 3

. Ok I found a hint in teh back of the book!!!!
each carbon atom in G is bonded to four other atoms in G because otherwise an additional hydrogen atom could be bonded to it and this would contradict teh ssumption that G has teh maximum number of hydrogen atoms for its number of carbon atoms. Also each hydrogen atom is bonded to exactly one carbon atom in G because otherwise G would not be connected.

Answer 4

but i obviously still dont know how to set it up as a proof

Answer 5

So we're assuming some value k for the number of carbon atoms, and assuming that the number of hydrogen atoms is maximal. Would you agree that this is part of the question?

Answer 6

what does maximal mean?

Answer 7

well the hydrogen atoms depend on teh carbon atoms

Answer 8

You can use maximal (almost) interchangeably with maximum

Answer 9

u know thsi stuff but just in case i drew a diagram of this

Answer 10

I imagine you would prove this using induction on the number of carbon atoms. Give me a minute to see if I get anywhere.

Answer 11

okkkkkkk thanks:D

Answer 12

This seems too easy....

You know that the total order of the graph is given by the sum of adjacent edges to each carbon atom, added to the sum of adjacent edges to each hydrogen atom. Since each carbon atom has 4 adjacent edges, that's \(4k\). Each hydrogen atom only has one adjacent edge, that's \(1m\).

This leaves us with \(4k+m\) as the total order.

Answer 13

U make everything easyyyyyyyyyy :DDDDDDDD
U R AWESOMMMMEEEEEEEE
Last nite i tried getting u the position as the king of OS

Answer 14

You're welcome, and thanks for the effort, I appreciate the thought :P

Answer 15

OMG IT WAS THAT EASYYYYYY hahahahahahah. Thanks kinggeorge that was soooo cleeaarrrr

Answer 16

You're welcome, that was far easier than I thought it would be =D