Let G be a simple graph and let S(G) be the subdivision graph of G, which is obtained from G by replacing each edge of G by a path of length two. In this paper, by the Principle of Inclusion and Exclusion we express the matching polynomial and Hosoya index of S(G) in terms of the matchings of G. Particularly, if G is a regular graph or a semi-regular bipartite graph, then the closed formulae of...

Let G be a simple graph with order n and size m. The quantity $$M_1(G)=\sum _{i=1}^{n}d^2_{v_i}$$ is called the first Zagreb index of G, where $$d_{v_i}$$ degree vertex $$v_i$$ , for all $$i=1,2,\dots ,n$$ . signless Laplacian matrix $$Q(G)=D(G)+A(G)$$ A(G) D(G) denote, respectively, adjacency diagonal degrees G. $$q_1\ge q_2\ge \dots \ge q_n\ge 0$$ eigenvalues largest eigenvalue $$q_1$$ spectr...

We study the problem of approximating value matching polynomial on graphs with edge parameter γ, where γ takes arbitrary values in complex plane. When is a positive real, Jerrum and Sinclair showed that admits an FPRAS general graphs. For Patel Regts, building methods developed by Barvinok, FPTAS maximum degree Δ as long not negative real number less than or equal to −1/(4(Δ −1)). Our first mai...

I have computed the matching polynomials of a number isomers fullerenes various sizes with objective developing molecular descriptors and similarity measures for on basis their polynomials. Two novel polynomial-based topological are developed, they demonstrated to discriminating power contrast closely related fullerenes. The ways place up seven disjoint dimers fullerene shown be identical, as n...

Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...

We consider an important class of dynamic singleinput single-output nonlinear systems where the system model is polynomial in observations but linear in parameters. The investigation is done in the errors-in-variables framework, i.e. both input and output are observed with noise. Assuming white Gaussian measurement noise that is characterized by a magnitude and a covariance structure, we propos...