INDEPENDENCE AND PI POLYNOMIALS FOR FEW STRINGS

If $s_k$ is the number of independent sets of cardinality $k$ in a graph $G$, then $I(G; x)= s_0+s_1x+…+s_{\alpha} x^{\alpha}$ is the independence polynomial of $G$ [ Gutman, I. and Harary, F., Generalizations of the matching polynomial, Utilitas Mathematica 24 (1983) 97-106] , where $\alpha=\alpha(G)$ is the size of a maximum independent set. Also the PI polynomial of a molecular graph $G$ is defined as $A+\sum x^{|E(G)|-N(e)}$, where $N(e)$ is the number of edges parallel to $e$, $A=|V(G)|(|V(G)|+1)/2-|E(G)|$ and summation goes over all edges of $G$. In [T. Do$\check{s}$li$\acute{c}$, A. Loghman and L. Badakhshian, Computing Topological Indices by Pulling a Few Strings, MATCH Commun. Math. Comput. Chem. 67 (2012) 173-190], several topological indices for all graphs consisting of at most three strings are computed. In this paper we compute the PI and independence polynomials for graphs containing one, two and three strings

CLUJ AND RELATED POLYNOMIALS IN BIPARTITE HYPERCUBE HYPERTUBES

A novel class of counting polynomials, called Cluj polynomials was proposed on the ground of Cluj matrices. The polynomial coefficients are calculated from the above matrices or by means of orthogonal edge-cuts. In this paper Cluj polynomial in bipartite hypercube hypertubes is presented. Definitions and relations with other polynomials and topological indices are derived

DOMINATION, TOTAL DOMINATION AND OPEN PACKING OF THE CORCOR DOMAIN OF GRAPHENE

A dominating set of a graph G = (V,E) is a subset D of V such that everyvertex not in D is adjacent to at least one vertex in D. A dominating set D is a totaldominating set, if every vertex in V is adjacent to at least one vertex in D. The set Pis said to be an open packing set if no two vertices of P have a common neighbor inG. In this paper, we obtain domination number, total domination number and openpacking number of the molecular graph of a new type of graphene named CorCor thatis a 2-dimensional carbon network

CLUJ AND RELATED POLYNOMIALS IN BIPARTITE HYPERCUBE HYPERTUBES

A novel class of counting polynomials, called Cluj polynomials was proposed on the ground of Cluj matrices. The polynomial coefficients are calculated from the above matrices or by means of orthogonal edge-cuts. In this paper Cluj polynomial in bipartite hypercube hypertubes is presented. Definitions and relations with other polynomials and topological indices are derived

ON (3,6) AND (4,6) - FULLERENE CAYLEY GRAPHS

An (r, s)-fullerene graph is a planar 3-regular graph with only Cr and Cs faces, where Cn denotes a cycle of length n. In this paper, the (3,6)-fullerene Cayley graphs constructed from finite groups are classified. A characterization of (4,6)-fullerene Cayley graphs is also presented

INDEPENDENCE AND PI POLYNOMIALS FOR FEW STRINGS

If $s_k$ is the number of independent sets of cardinality $k$ in a graph $G$, then $I(G; x)= s_0+s_1x+…+s_{\alpha} x^{\alpha}$ is the independence polynomial of $G$ [ Gutman, I. and Harary, F., Generalizations of the matching polynomial, Utilitas Mathematica 24 (1983) 97-106] , where $\alpha=\alpha(G)$ is the size of a maximum independent set. Also the PI polynomial of a molecular graph $G$ is defined as $A+\sum x^{|E(G)|-N(e)}$, where $N(e)$ is the number of edges parallel to $e$, $A=|V(G)|(|V(G)|+1)/2-|E(G)|$ and summation goes over all edges of $G$. In [T. Do$\check{s}$li$\acute{c}$, A. Loghman and L. Badakhshian, Computing Topological Indices by Pulling a Few Strings, MATCH Commun. Math. Comput. Chem. 67 (2012) 173-190], several topological indices for all graphs consisting of at most three strings are computed. In this paper we compute the PI and independence polynomials for graphs containing one, two and three strings.</jats:p

Bending and buckling behaviors of heterogeneous temperature-dependent micro annular/circular porous sandwich plates integrated by FGPEM nano-Composite layers

Bending and buckling analyses of heterogeneous annular/circular micro sandwich plate which is located on Pasternak substrate is presented in the current study. The plate’s core is made of saturated porous materials and face sheets are made of functionally graded piezo-electro-magnetic polymeric nano-composites. The displacement components of the plate described based on FSDT and MCST is employed to analyze the structure in micro scale. Length scale parameter of MCST shows the difference between macro and micro scales elasticity theory. Material properties of the three layers are varied across the thickness following different patterns and in addition, are temperature-dependent. The face sheets are subjected to electro-magnetic fields and pre loads. Using energy method and variational calculus, the equations are obtained and solved via GDQ as a numerical method for various boundary conditions. To examine the reliability of the results, they are compared with previous studies and verified. Effect of different properties and aspect ratio of the plate are investigated and highlighted. The results depicted by enhancing the porosity, the critical buckling load and maximum transverse deflection decreases and increases, respectively. Also increasing temperature leads the buckling load to more values and vice versa about deflection of the plate. The findings of this research can help to design and create more efficient structures especially smart one as sensors or actuators. </jats:p