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The topological indices $irr(G)$ related to the \emph{first Zagreb index,}$M_1(G)$ and the \emph{second Zagreb index,} $M_2(G)$ are the oldestirregularity measures researched. Alberton $[3]$ introduced the\emph{irregularity} of $G$ as $irr(G) = \sum\limits_{e \in E(G)}imb(e), imb(e)= |d(v) - d(u)|_{e=vu}$. In the paper of Fath-Tabar $[7]$, Alberton's indicewas named the \emph{third Zagreb indice} to conform with the terminology ofchemical graph theory. Recently Ado et.al. $[1]$ introduced the topologicalindice called \emph{total irregularity}. The latter could be called the\emph{fourth Zagreb indice}. we define the $\pm$\emph{Fibonacci weight,}$f^\pm_i$ of a vertex $v_i$ to be $-f_{d(v_i)},$ if $d(v_i)$ is uneven and$f_{d(v_i)}$, if $d(v_i)$ is even. From the aforesaid we define the$f^\pm$-Zagreb indices. This paper presents introductory results for theundirected underlying graphs of Jaco Graphs, $J_n(1), n \leq 12$. For more onJaco Graphs $J_n(1)$ see $[9, 10]$. Finally we introduce the \emph{Khazamulairregularity} as a new topological variant.

A note on $f^\pm$-Zagreb indices in respect of Jaco Graphs, $J_n(1), n \in \Bbb N$ and the introduction of Khazamula irregularity