Survey on Sum Graphs

Most papers thus far on sum graphs have involved finding the sum number for a particular class of graphs. These include

• $\sigma(K_n)=2n-3$ for $n \ge 4$ [#!bhhjkw!#]
• $\sigma(K_{m,n})= {{\lceil 3m+n-3\rceil} \over {2}}$ for $n \ge m \ge 2$ [#!hs1!#]
• $\sigma (H_{2,n})=4n-5$ for $n \ge 2$ [#!rms!#]
• $\sigma (C_n)=2$ for $n \ne 4$ [#!h!#]
• $\sigma (W_n)= {n \over 2} +2$ for even $n \ge 4$,      $\sigma (W_n)=n$ for odd $n\ge5$ [#!hs2!#]
• $\sigma(F_n) =1$ for all $n \ge 2$ [#!e!#]