We generalize several topological indices and introduce the general degree distance of a connected graph $G$. For $a, b \in \mathbb{R}$, $DD_{a,b} (G) = \sum_{ v V(G)} [deg_{G}(v)]^a S^b_{G} (v)$, where $V(G)$ is vertex set $G$, $deg_G (v)$ $v$, $S^b_{G} (v) w V(G) \setminus \{ \} } [d_{G} (v,w) ]^{b}$ $d_{G} (v,w)$ between $v$ $w$ in present some sharp bounds on for multipartite graphs trees g...

We develop a two-stage experimental protocol by which i) we elicit the social network within a group of undergraduate students and ii) we measure their altruistic attitudes by way of a standard Dictator game. We observe that more socially integrated subjects are also more altruistic, as betweenness centrality and reciprocal degree are positively correlated with the level of giving, even after c...

In this paper, we determine the degree distance of the complement of arbitrary Mycielskian graphs. It is well known that almost all graphs have diameter two. We determine this graphical invariant for the Mycielskian of graphs with diameter two.

Measuring consistency of preferences is very important in decision-making. This paper addresses this key issue for interval-valued reciprocal preference relations. Existing studies implement one of two different measures: the “classical” consistency measure, and the “boundary” consistency measure. The classical consistency degree of an interval-valued reciprocal preference relation is determine...