the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...

Graph invariants, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. The degree resistance distance of a graph G is defined as D R (G) =  {u,v}⊆V (G) [d(u) + d(v)]R(u, v), where d(u) is the degree of the vertex u, and R(u, v) the resistance distance between the vertices u and v. Let Cact(n; t) be the set of all cacti possessing n vertices and t cy...

Recently in [1], the authors have given a method for calculation of the effective resistance (resistance distance) on distance-regular networks, where the calculation was based on stratification introduced in [2] and Stieltjes transform of the spectral distribution (Stieltjes function) associated with the network. Also, in Ref. [1] it has been shown that the resistance distances between a node ...

the effect of inter-implant distance on retention and resistance of implant-tissue-supported overdentures is lacking in the literature. an in vitro study was performed to evaluate this effect for mandibular implant-tissue-supported overdentures retained by two ball attachments.an acrylic cast of an edentulous mandible was fabricated. three pairs of implants were symmetrically placed at both sid...