The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) Merris (2002), threshold split form upward-closed sets within they belong to, i.e., any sequence majorizing a or must itself be threshold, respectively. Motivated fact that have characterizations in terms forbidden induced subgraphs, we define class $\ma...

Distance properties of molecular graphs form an important topic in chemical graph theory.1 To justify this statement just recall the famous Wiener index which is also known as the Wiener number. This index is the first2 but also one of the most important topological indices of chemical graphs. Its research is still very active; see recent reviews3,4 and several new results in a volume5 dedicate...

This research is motivated by the existence of an online learning process during Covid 19 pandemic, so it necessary to understand that can increase student motivation. In there are many obstacles cause discussion be not very effective and efficient students' motivation in also decreases their achievement decreases. study aims determine level pandemic. type uses a quantitative approach using sur...

1. Wisner DM, Quillen DA, Benderson DM, Green MJ. Patient attitudes toward resident involvement in cataract surgery. Arch Ophthalmol. 2008;126(9):12351239. 2. Vallance JH, Ahmed M, Dhillon B. Cataract surgery and consent: recall, anxiety, and attitude toward trainee surgeons preoperatively and postoperatively. J Cataract Refract Surg. 2004;30(7):1479-1485. 3. Versluis MA, van der Linden PJ. Pat...

Let G be a finite, undirected, and simple graph. If {v1, · · · , vn} is the set of vertices of G, then the adjacency matrix A(G) = [aij ] is an n-by-n matrix where aij = 1 if vi and vj are adjacent and aij = 0 otherwise. The energy of a graph, E(G), is defined as the sum of the absolute values of eigenvalues of A(G). The concept of energy originates in chemistry and was first defined by I. Gutm...

If sk equals the number of stable sets of cardinality k in the graph G, then I(G; x) = α(G) ∑ k=0 skx k is the independence polynomial of G (Gutman and Harary, 1983). Alavi, Malde, Schwenk and Erdös (1987) conjectured that I(G; x) is unimodal whenever G is a forest, while Brown, Dilcher and Nowakowski (2000) conjectured that I(G; x) is unimodal for any well-covered graph G. Michael and Traves (...

Given two graphs G and H, assume that C = {C1, C2, . . . , Cq} is a clique cover of G and U is a subset of V (H). We introduce a new graph operation called the clique cover product, denoted by G ⋆ HU , as follows: for each clique Ci ∈ C , add a copy of the graph H and join every vertex of Ci to every vertex of U . We prove that the independence polynomial of G ⋆ HU I(G ⋆ H ;x) = I(H;x)I(G; xI(H...