The notion of a fractional Cartesian product and a subsequent notion of combinatorial dimension appeared first in a harmonic-analytic context in the course of filling ”analytic” gaps between successive (ordinary) Cartesian products of spectral sets [1, 2]. (Detailed accounts of this, and much more, appear in [4].) Combinatorial dimension is an index of interdependence: attached to a subset of a...

bandwidth labelling is a well known research area in graph theory. we provide a new proof that the bandwidth of mobius ladder is 4, if it is not a $k_{4}$, and investigate the bandwidth of a wider class of mobius graphs of even strips.

The distance $d(u,v)$ between two vertices $u$ and $v$ of a graph $G$ is equal to the length of a shortest path that connects $u$ and $v$. Define $WW(G,x) = 1/2sum_{{ a,b } subseteq V(G)}x^{d(a,b) + d^2(a,b)}$, where $d(G)$ is the greatest distance between any two vertices. In this paper the hyper-Wiener polynomials of the Cartesian product, composition, join and disjunction of graphs are compu...