Question: Let $H$ be a graph of order 10 such that $3\le d(v)\le5$ for each vertex $v$ in $H$ [where $d(v)$ is the degree of $v$]. Not every vertex is of even degree. No two odd-degree vertices are of the same degree. What is the size [number of edges] of $H$?
Answer: Size of $H$ is 20
let $V(H)=\{{a,b,c,d,e,f,g,h,i,j\}}$, then $d(a)=3, d(b)=4, d(c)=4, d(d)=4, d(e)=4, d(f)=4, d(g)=4, d(h)=4, d(i)=4,$ $d(j)=5$
Sum is 40
hence size is 20
Am I correct?