let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

Indirect reciprocity occurs when the cooperative behavior between two individuals is contingent on their previous behavior toward others. Previous theoretical analysis indicates that indirect reciprocity can evolve if individuals use an image-scoring strategy. In this paper, we show that, when errors are added, indirect reciprocity cannot be based on an image-scoring strategy. However, if indiv...

Friendship plays a critical role in social commerce in contemporary societies. This study aims to theorize and examine how friendship quality impacts purchase intention. Product-related risk is introduced to gain insight into its moderating effects on intention to purchase from three different seller groups. Through empirical evidence, we confirm that friendship quality has positively effect on...

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...

Difficulties in friendships have been reported both in people with Autism Spectrum Disorder (ASD) and in individuals with Anorexia Nervosa (AN). This small-scale qualitative study aimed to evaluate the friendship experiences of seven patients with AN who presented with possible ASD traits; to determine whether their experiences were reflective of those found in people with ASD, and whether any ...

The authors examined associations of perceived similarity, actual similarity, and peer-rated similarity in personality with friendship intensity during the acquaintanceship process in a naturalistic setting. Self- and peer-rated personality data were gathered from undergraduates (mean age = 18.9) at 5 time points during the first year of university using a round-robin design. Whereas perceived ...