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...

In this paper we study the problem of conditioning a belief function b with respect to an event A by geometrically projecting such belief function onto the simplex associated with A in the simplex of all belief functions. Two different such simplices can be defined, as each belief function can be represented as the vector of its basic probability values or the vector of its belief values. We sh...

In this paper we investigate the complexity of model selection and model testing in chemical reaction networks by formulating them as Euclidean distance problems. We determine closed form expressions for the Euclidean distance degree of the steady state varieties associated to several different families of toric chemical reaction networks with arbitrarily many reaction sites. We show how our re...

If G is a connected graph with vertex set V , then the degree distance of G, D′(G), is defined as ∑ {u,v}⊆V (deg u + deg v) d(u, v), where degw is the degree of vertex w, and d(u, v) denotes the distance between u and v. We prove the asymptotically sharp upper bound D′(G) ≤ 14 nd(n− d) 2 +O(n7/2) for graphs of order n and diameter d. As a corollary we obtain the bound D′(G) ≤ 1 27 n 4 + O(n7/2)...

Energy consumption is an important parameter in the context of the wireless sensor networks (WSNs). Several factors can cause energy over consumption such as mobility, node position (relay or gateway), retransmissions... In this paper, we described a new Energy-Degree Distance(EDD) Clustering Algorithm for the WSNs. A node with higher residual energy, higher degree and closer to the base statio...

The degree distance of a graph which is a degree analogue of the Wiener index of the graph. Let G = TUV C6[2p, q] be the carbon nanotubes covered by C6, formulas for calculating the degree distance of armchair polyhex nanotubes TUV C6[2p, q] are provided. Mathematics Subject Classification: 05C05, 05C12

Let G be a connected graph with vertex set V (G). The degree resistance distance of G is defined as DR(G) = ∑ fu,vg V (G)[d(u) +d(v)]R(u, v), where d(u) is the degree of vertex u, and R(u, v) denotes the resistance distance between u and v. In this paper, we characterize n-vertex unicyclic graphs having minimum and second minimum degree resistance distance.