In order to solve effectively the problem of evaluating the wireless sensor network fault tolerance, this paper presents an evaluation index of the topological tolerance for failure node according to the ability of the topology keeping network connect and cover in case of existing failure nodes and establishes a quantitative evaluation model of topology fault tolerance according to semi-Markov ...

In this paper, we compute topological indices of the total graphs of the tadpole graphs, wheel graphs and ladder graphs using the subdivision concept, which extend the results of Ranjini et al. (2011).

We consider topological indices I that are sums of f(deg(u))f(deg(v)), where {u, v} are adjacent vertices and f is a function. The Randić connectivity index or the Zagreb group index are examples for indices of this kind. In earlier work on topological indices that are sums of independent random variables, we identified the correlation between I and the edge set of the molecular graph as the ma...

‎the narumi-katayama index was the first topological index defined‎ ‎by the product of some graph theoretical quantities‎. ‎let $g$ be a ‎simple graph with vertex set $v = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $g$‎. ‎the narumi-katayama ‎index is defined as $nk(g) = prod_{vin v}d(v)$‎. ‎in this paper,‎ ‎the narumi-katayama index is generalized using a $n$-ve...

‎    The Narumi-Katayama index is the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph. Narumi-Katayama index of G is defined as the product of the degrees of the vertices of G. In this paper, we define the Narumi-Katayama polynomial of G. Next, we investigate some properties of this polynomial for graphs and then, we obtain ...

SU(3) gauge theory in the 2-index symmetric (sextet) and fundamental representations is considered in symmetric and periodic boxes. Using the overlap formulation in the quenched approximation it is shown that the topological charge obtained from the sextet index theorem always leads to an integer value and agrees with the charge obtained from the fundamental index theorem in the continuum. At l...

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...

The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are sufficient to characterize the coincidence index in the setting of continuous m...

Mathematical descriptors of molecular structure, such as various topological indices, have been widely used in structure-property-activity studies (see [5, 6, 12]). Among the numerous topological indices considered in chemical graph theory, only a few have been found noteworthy in practical application (see [10]). One of these is the connectivity index or Randić index. The Randić index of an or...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...