Let G = (V,E) be a simple graph. An edge labeling f : E → {0, 1} induces a vertex labeling f : V → Z2 defined by f(v) ≡ ∑ uv∈E f(uv) (mod 2) for each v ∈ V , where Z2 = {0, 1} is the additive group of order 2. For i ∈ {0, 1}, let ef (i) = |f−1(i)| and vf (i) = |(f+)−1(i)|. A labeling f is called edge-friendly if |ef (1) − ef (0)| ≤ 1. If (G) = vf (1) − vf (0) is called the edge-friendly index o...

We consider the full multinomial combinatorics of all irreducible representations of the octahedral (cubic) symmetry as a function of partitions for vertex, face and edge colorings. Full combinatorial tables for all irreducible representations and all multinomial partitions are constructed. These enumerations constitute multinomial expansions of character-based cycle index polynomials, and grow...

This paper demonstrates a real-time, full-3D edge tracker based on a particle filter. In contrast to previous methods this system is capable of tracking complex self-occluding three-dimensional structures. The system exploits graphics hardware in a novel manner, allowing it not only to perform hidden line removal for each particle but also to evaluate pose likelihoods directly on the graphics c...

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...

Most research on computer vision (CV)-based vibration measurement is limited to the determination of discrete or coarse mode shapes structure. The continuous edge structure in images has rich optical features, and thus, by identifying tracking movement structure’s edge, it possible determine high-resolution full-field without a preset target. present study proposes CV-based method shape identif...