the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

Two longitudinal studies examined associations between relational aggression and friendship quality during adolescence. In Study 1, 62 adolescents in Grades 6 (25.8%), 7 (32.3%), and 8 (41.9%) completed assessments of friendship affiliations, relational and overt aggression, and friendship quality at 2 time points, 1 year apart. Results using actor partner interdependence modeling indicated tha...

The study examined whether reciprocal friendship quantity or quality can mitigate genetic vulnerability for depression symptoms in children. The sample comprised 168 monozygotic twin pairs and 126 same-sex dizygotic twin pairs assessed in Grade 4 (mean age = 10.04 years). Friendship participation was measured via reciprocal nominations of close friendships within the classroom. Friendship quali...

Abstract The clustering coefficient has been introduced to capture the social phenomena that a friend of tends be my friend. This metric widely studied and shown great interest describe characteristics graph. But, is originally defined for graph in which links are undirected, such as friendship (Facebook) or professional (LinkedIn). For directed from source information consumer information, it ...

Suppose that G is a graph with n vertices and m edges, and let be the spectral radius of its adjacency matrix. Recently we showed that if G has no 4-cycle, then 2 n 1; with equality if and only if G is the friendship graph. Here we prove that if m 9 and G has no 4-cycle, then 2 m; with equality if G is a star. For 4 m 8 this assertion fails. Keywords: 4-cycles; graph spectral radius; graphs wit...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.