Majority neighbor sum distinguishing conjecture

Let $G$ be a graph with minimum degree $\delta(G)\geq 2$, and let $\chi_{\sum}^{M}(G)$ denote its majority neighbor sum distinguishing index. Majority neighbor sum distinguishing conjecture. Every graph $G$ with $\delta(G)\geq 2$ satisfies

$$\chi_{\sum}^{M}(G)\leq 5.$$

This conjecture is posed after bounds for majority neighbor sum distinguishing colorings, including a bound of 15 for graphs of minimum degree at least 4 and 12 for even-order graphs whose vertices all have even degree; its resolution is not given in the supplied text.