m-polynomial and degree-based topological indices
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abstract
let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the $m$-polynomial. the new approach is also illustrated with examples.
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Journal title:
iranian journal of mathematical chemistryPublisher: university of kashan
ISSN 2228-6489
volume 6
issue 2 2015
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