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welcome back to discrete mathematics - today were going to take a look at vertex degree and some other very closely related theorems so what is a degree well every vertex has a degree which we abbreviate as dig with our vertex as its argument and thats the number of edges in the graph that are incident to that vertex so for instance I have a nice small graph here its got three vertices and three edges so we take a look at what is the degree of a well heres a heres a vertex a and has one edge incident to it so the degree of a is one but what about B well B has the edge going to a thats incident and has an edge going to C so the degree of B is two so what about C okay well we see that C has an edge going to be so thats one but what do we do when it loops okay well when it loops we have C leaving and C entering again so we have two points that it goes through so if we take a look at lets say this pair is C C so this is what the edge looks like in our edge set then its degree get
