Conjecture on the super edge-magic total strength of odd-cycle unicyclic graphs

Let $G(n;k_{1},\dots,k_{n})$ be the super edge-magic total unicyclic $(p,q)$-graph consisting of an odd cycle

$$C_n=\{a_1,a_2,\dots,a_n\}$$

and $k_i$ pendant vertices adjacent to each $a_i$, for $1\leq i\leq n$. Here $s m(G)$ denotes the super edge-magic total strength of $G$. Super edge-magic total strength conjecture.

$$s m(G(n;k_{1},\dots,k_{n}))=2q+\frac{n+3}{2}.$$

The claim extends the known exact value for the uniform family $k_i=k$, while the paper presents computations for certain graphs in this broader family as supporting evidence; its general validity remains open.