The friendship paradox is revisited by considering both local and global averages of friends. How the economics of attention affects the recruitment of friends is examined. Statistical implications of varying individual attentions are investigated and it is argued that this is one reason why the mean of friends is higher than the median in social networks. The distribution of friends skews to t...

The rank of a graph is defined to be the its adjacency matrix. A called reduced if it has no isolated vertices and two with same set neighbors. G said maximal any containing as proper induced subgraph higher rank. main intent this paper present some results on graphs. First, we introduce characterization trees (a tree not subtree rank). Next, give near-complete ‘generalized friendship graphs.’ ...

Our friends have more friends than we do. That is the basis of the friendship paradox. In mathematical terms, the mean number of friends of friends is higher than the mean number of friends. In the present study, we analyzed the relationship between the mean degree of vertices (individuals), 〈k〉, and the mean number of friends of friends, 〈kFF 〉, in scale-free networks with degrees ranging from...

For a simple, undirected graph G with, at most one isolated vertex and no edges, labeling f:E(G)→{1,2,…,k1} of positive integers to the edges is called irregular if weights each has different value. The integer k1 then irregularity strength G. If number vertices in or order |G|, μ:E(G)→{1,2,…,k2} modular remainder divided by |G| k2 disjoint union two more graphs, denoted ‘+’, an operation where...

Received: December 16, 2010 Accepted: December 31, 2010 doi:10.5539/jmr.v3n2p206 Abstract In this paper we investigate product cordial labeling for some new graphs. We prove that the friendship graph, cycle with one chord (except when n is even and the chord joining the vertices at diameter distance), cycle with twin chords (except when n is even and one of the chord joining the vertices at dia...

A graph G is H-saturated if G does not contain H as a subgraph but for any nonadjacent vertices u and v, G+uv containsH as a subgraph. The parameter sat(H, n) is theminimum number of edges in an H-saturated graph of order n. In this paper, we determine sat(H, n) for sufficiently large nwhen H is a union of cliques of the same order, an arbitrary union of two cliques and a generalized friendship...

For integers k > 0 and r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex v of degree d(v) in G is adjacent to vertices with at least min{r, d(v)} different colors. The smallest integer k for which a graph G has a conditional (k, r)-coloring is called the rth order conditional chromatic number, denoted by χr(G). For different val...

Many networks and accordingly their representation in graphs are subject to structural changes during the course of their existence [CKT06]. Examples for such evolutionary networks include friendship networks in online communities, co-authorship networks in the scientific domain and collocation networks in computational linguistics. Studying the evolution of such networks can provide vital data...