Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.

The generalized k-connectivity κk(G) of a graphG, which was introduced by Chartrand et al.(1984) is a generalization of the concept of vertex connectivity. Let G and H be nontrivial connected graphs. Recently, Li et al. gave a lower bound for the generalized 3-connectivity of the Cartesian product graph G H and proposed a conjecture for the case that H is 3-connected. In this paper, we give two...

Various product operations are employed for constructing larger networks from smaller ones, among which direct-product operation is the most frequently employed one. The direct product of two graphs G1 andG2, denoted byG1×G2, is defined on vertex set V G1 ×V G2 , where two vertices x1, x2 and y1, y2 are adjacent to each other in G1 × G2 if and only if x1y1 ∈ E G1 and x2y2 ∈ E G2 . Other names f...

Introduction: Long-term stressful situations can drastically influence one’s mental life. However, the effect of mental stress on recognition of emotional stimuli needs to be explored. In this study, recognition of emotional stimuli in a stressful situation was investigated. Four emotional conditions, including positive and negative states in both low and high levels of arousal were analy...

For a connected graph G = (V (G), E(G)), a vertex set S ⊆ V (G) is a k-restricted vertex-cut if G − S is disconnected such that every component of G − S has at least k vertices. The k-restricted connectivity κk(G) of the graph G is the cardinality of a minimum k-restricted vertex-cut of G. In this paper, we give the 3-restricted connectivity and the 4-restricted connectivity of the Cartesian pr...

The sum-connectivity index R′(G) of a graph G is the sum of the weights (du +dv) − 2 of all edges uv of G, where du and dv are the degrees of the vertices u and v in G. This index was recently introduced in [B. Zhou, N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46(2009), 1252–1270]. In this paper, we give the sharp lower bound of the sum-connectivity index of n-vertex unicyclic ...

in this paper, some applications of our earlier results in working with chemical graphs arepresented.

For a 2-edge-connected graph G, the group connectivity number of G is defined as Λg(G) = min{k : G is A-connected for every abelian group with |A| ≥ k}. Let G •H denote the semistrong product of two graphs G and H. In this paper, we extend the result of Yan et al. [Int. J. Algebra 4 (2010), 1185–1200] on group connectivity in Cartesian product of graphs to semistrong products and make a slightl...