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- W2104408875 abstract "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 oldest irregularity measures researched. Alberton $[3]$ introduced the emph{irregularity} of $G$ as $irr(G) = sumlimits_{e in E(G)}imb(e), imb(e) = |d(v) - d(u)|_{e=vu}$. In the paper of Fath-Tabar $[7]$, Alberton's indice was named the emph{third Zagreb indice} to conform with the terminology of chemical graph theory. Recently Ado et.al. $[1]$ introduced the topological indice 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 the undirected underlying graphs of Jaco Graphs, $J_n(1), n leq 12$. For more on Jaco Graphs $J_n(1)$ see $[9, 10]$. Finally we introduce the emph{Khazamula irregularity} as a new topological variant." @default.
- W2104408875 created "2016-06-24" @default.
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- W2104408875 date "2014-07-31" @default.
- W2104408875 modified "2023-09-25" @default.
- W2104408875 title "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" @default.
- W2104408875 cites W188720847 @default.
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- W2104408875 doi "https://doi.org/10.48550/arxiv.1407.8290" @default.
- W2104408875 hasPublicationYear "2014" @default.
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