Computations of the M-Polynomials and Degree-Based Topological Indices for Dendrimers and Polyomino Chains
نویسندگان
چکیده
منابع مشابه
M-polynomial and degree-based topological indices
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 ca...
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We show that the zig-zag chain Z3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {φij} under which the zig-zag chain Z3 n is an extremal value of the induced topological index T defined by T (G) = ∑ 1≤i≤j≤n−1 mijφij where G is a graph with n vertices and mij is the number of edges of...
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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 ca...
متن کاملM-Polynomial and Degree-Based Topological Indices
Let G be a graph and let mij(G), i, j ≥ 1, be the number of edges uv of G such that {dv(G), du(G)} = {i, j}. TheM -polynomial ofG is introduced withM(G;x, y) = ∑ i≤j mij(G)x y . 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 -polyn...
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Mobeen Munir 1, Waqas Nazeer 1, Shazia Rafique 2 and Shin Min Kang 3,4,* 1 Division of Science and Technology, University of Education, Lahore 54000, Pakistan; [email protected] (M.M.); [email protected] (W.N.) 2 Center for Excellence in Molecular Biology, Punjab University Lahore, Lahore 53700, Pakistan; [email protected] 3 Department of Mathematics and Research Institute of Natural ...
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ژورنال
عنوان ژورنال: International Journal of Analytical Chemistry
سال: 2018
ISSN: 1687-8760,1687-8779
DOI: 10.1155/2018/1709073