Einen guten Überblick über Anzahlen von Knotenfärbungen eines Graphen findet der Leser in der grundlegenden Monografie von Norman Biggs(1). Bei der Untersuchung von Knotenfärbungen ausgewählter Graphen und deren Anzahlen ergaben sich verschiedene 0-1-Matrizen mit interessanten Eigenschaften. Diese sollen,…
Fibonacci Folge, Rechteckdarstellung einer Teilfolge, Eisenstein-Stern-Brocot-Funktion, verallgemeinerte Eisenstein-Stern-Brocot-Funktion, reelle Nullstellen und Lage der komplexen Nullstellen, gerichtete Graphen und deren Matrizen, reziproke und negativreziproke Polynome
A (k, 6)-cage (k = 2, 3, 4, 5) is a 2-connected cubic plane graph that has only k-gons and hexagons as its faces. Continuing their work on (3, 6)-cages (2009) the authors investigate the combinatorial (topological and algebraic) structure of (2, 6)-cages and explicitly determine their eigenvalues and…
Davidson (1981) developed a general procedure, based on group representation theory, for determining the spectra of graphs distinguished by a certain rotational symmetry, with application to molecular graphs. In this paper a more general method, applicable to any arbitrarily arc weighted directed graph…
An n-fold periodic locally finite graph in the euclidean n-space may be considered the parent of an infinite class of n-dimensional toroidal finite graphs. An elementary method is developed which allows the characteristic polynomials of these graphs to be factored, in a uniform manner, into smaller polynomials,…
The Padmakar-Ivan (PI) index of a graph G is defined as PI (G) = Σ [neu(e|G)+nev(e|G)], where for edge e=(u,v) are neu (e|G) the number of edges of G lying closer to u than v, and nev (e|G) is the number of edges of G lying closer to v than u and summation goes over all edges of G. The PI index is a…
In August 2003 the computer program GRAFFITI made conjecture 1001 stating that for any benzenoid graph, the size of a maximum matching equals the number of positive eigenvalues. Later, the authors learned that this conjecture was already known in 1982 to I. Gutman (Kragujevac). Here we present a proof…
Dürer's engraving Melencolia I famously includes a perspective view of a solid polyhedral block of which the visible portion is an 8-circuit bounding a pentagon-triple+triangle patch. The polyhedron is usually taken to be a cube truncated on antipodal corners, but an infinity of others are compatible…