A total k-labeling is a function fe from the edge set to {1, 2, . , ke} and fv vertex {0, 4, 2kv}, where k = max{ke, 2kv}. distance irregular reflexive of graph G k-labeling, if for every two different vertices u 0 G, w(u) 6= w(u ), Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum which has k-labelling called strength denoted by Dref (G). In this paper, we determine exact value some connected graph...

ON GRAPHS SATISFYING A STRONG ADJACENCY PROPERTY Y. Ananchuen and L. Caccetta School of Mathematics and Statistics Curtin University of Technology GPO Box U1987 Perth 6001 Western Australia. Dedicated to the memory of Alan Rahilly, 1947 1992 Let m and n be nonnegative integers and k be a positive integer. A graph G is said to have property P*(m,n,k) if for any set of m + n distinct vertices of ...

The “friendship paradox” (Feld (1991)) refers to the fact that, on average, people have strictly fewer friends than their friends have. I show that this over-sampling of the most popular people amplifies behaviors that involve complementarities. People with more friends experience greater complementarities and hence take more extreme actions. Given the friendship paradox, people then perceive m...

Friendships are essential for adolescent social development. However, they may be pursued for varying motives, which, in turn, may predict similarity in friendships via social selection or social influence processes, and likely help to explain friendship quality. We examined the effect of early adolescents' (N = 374, 12-14 years) intrinsic and extrinsic friendship motivation on friendship selec...

Background: There is still a question of whether online friendship predicts changes in face-to-face friendship (Reduction Hypothesis) or face-to-face friendship predicts changes in online friendship (Compensation Hypothesis) during adolescence. Objective: The purpose of this study was to compare these two hypotheses to determine which comes first: online friendship or offline friendship. Method...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

For any simple graph H, let σ(H,n) be the minimum m so that for any realizable degree sequence π = (d1, d2, . . . , dn) with sum of degrees at least m, there exists an n-vertex graph G witnessing π that contains H as a weak subgraph. Let Fk denote the friendship graph on 2k+1 vertices, that is, the graph of k triangles intersecting in a single vertex. In this paper, for n sufficiently large, σ(...