Background: Ensuring adequate depth of anesthesia during surgery is essential for anesthesiologists to prevent the occurrence of unwanted alertness during surgery or failure to return to consciousness. Since the purpose of using anesthetics is to affect the central nervous system, brain signal processing such as electroencephalography (EEG) can be used to predict different levels of anesthesia....

let g be a graph. in this paper, we study the eccentric connectivity index, the new version ofthe second zagreb index and the forth geometric–arithmetic index.. the basic properties ofthese novel graph descriptors and some inequalities for them are established.

The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for  ABCa index for cacti of order $n$ ...

Let m be a positive integer and let G be a cubic graph of order 2n. We consider the problem of covering the edge-set of G with the minimum number of matchings of size m. This number is called the excessive [m]-index of G in the literature. The case m = n, that is, a covering with perfect matchings, is known to be strictly related to an outstanding conjecture of Berge and Fulkerson. In this pape...

The present note is devoted to establish some extremal results for the zerothorder general Randić index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

Let T ∆ n denote the set of trees of order n, in which the degree of each vertex is bounded by some integer ∆. Suppose that every tree in T ∆ n is equally likely. We show that the number of vertices of degree j in T ∆ n is asymptotically normal with mean (μj + o(1))n and variance (σj + o(1))n, where μj , σj are some constants. As a consequence, we give estimate to the value of the general Zagre...

The general Randić index Rα(G) is the sum of the weight d(u)d(v)α over all edges uv of a graph G, where α is a real number and d(u) is the degree of the vertex u of G. In this paper, for any real number α = 0, the first three minimum general Randić indices among trees are determined, and the corresponding extremal trees are characterized.