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- W4288601296 abstract "The modified Albertson index, denoted by $A!^*!$, of a graph $G$ is defined as $A!^*!(G)=sum_{uvin E(G)} |(d_{u})^{2}- (d_{v})^{2}|$, where $d_u$, $d_v$ denote the degrees of the vertices $u$, $v$, respectively, of $G$ and $E(G)$ is the edge set of $G$. In this note, a sharp lower bound of $A!^*$ in terms of the maximum degree for the case of trees is derived. The $n$-vertex trees having maximal and minimal $A!^*$ values are also characterized here. Moreover, it is shown that $A!^*!(G)$ is non-negative even integer for every graph $G$ and that there exist infinitely many connected graphs whose $A!^*$ value is $2t$ for every integer $tin{0,3,4,5}cup{8,9,10,cdots}$." @default.
- W4288601296 created "2022-07-29" @default.
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- W4288601296 date "2019-02-05" @default.
- W4288601296 modified "2023-09-30" @default.
- W4288601296 title "A Note on the Modified Albertson Index" @default.
- W4288601296 doi "https://doi.org/10.48550/arxiv.1902.01809" @default.
- W4288601296 hasPublicationYear "2019" @default.
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