Polygonal Graphs

Author(s):  
Ákos Seress
Keyword(s):  
2010 ◽  
Vol 68 (3) ◽  
pp. 246-254 ◽  
Author(s):  
Ákos Seress ◽  
Eric Swartz

2012 ◽  
Vol 16 (4) ◽  
pp. 891-903
Author(s):  
Ákos Seress ◽  
Eric Swartz
Keyword(s):  

1979 ◽  
Vol 31 (6) ◽  
pp. 1307-1321 ◽  
Author(s):  
Manley Perkel

In this paper we investigate the action of finite groups G on finite polygonal graphs. The notion of a polygonal graph was introduced in [17]: A polygonal graph is a pair (, ) consisting of a graph which is regular, connected and has girth m for some m ≧ 3, and a set of m-gons of such that every 2-claw of is contained in an unique element of (See Section 2 for the définitions of the terms used here.) If is the set of all m-gons of , so that there is in an unique m-gon on every one of its 2-claws, then we write for (, ) and call a strict polygonal graph. If we wish to emphasize the integer m, then we call (, ) an m-gon-graph (respectively, a strict m-gon-graph).


2013 ◽  
Vol 159 (2) ◽  
pp. 361-396
Author(s):  
Markku Tykkyläinen

Relative, mean and integral accessibility in the existing provinces of Finland and in the proposed new provinces was studied applying graph theory, through evaluating the shapes of the provinces by reference to polygonal graphs, and, in a more detailed analysis, through using flow graphs to represent the accessibility between locations. The sensitivity of the ac­cessibility structure was tested by means of two simulation experiments. The poorest accessibility levels existed in the more northerly provinces, although some provinces weak in this respect could also be found in Southern and Central Finland, especially when accessibility was studied in relation to the size of the province. This correlates with a certain backwardness in the development of the administrative regions in relation to population development. The proposed province revisions have not corrected this situation entirely. The locations of the provincial capitals are close to the (pareto‑)optimum in general, the non‑optimal cases being ones in which the most significant centres of population growth have been located elsewhere than in the provincial capital or its immediate sur­roundings. Integral accessibility as a measure of optimal location is not sensitive to changes in spatial structure, and extremely large movements of population would be required to cause any substantial alteration in the location of the optimal centre.


1970 ◽  
Vol 48 (12) ◽  
pp. 2241-2247 ◽  
Author(s):  
Alexandra Glashan Guerriero ◽  
W. F. Grant ◽  
W. H. Brittain

A cytological and morphological study using hybrid indices, pictorialized scatter diagrams, and polygonal graphs has been carried out on a collection of Betula cordifolia Regel, B. populijolia Marsh., and some hybrids of these two species × B. caerulea Blanch. (B. caerulea Blanch, and B. caerulea-grandis Blanch.). A somatic chromosome number of 28 was determined for plants of all accession numbers of these taxa. Measurements of morphological characters were also made on plants of B. papyrifera Marsh. Hybrid index values, a pictorialized scatter diagram, and polygons showed that plants of B. caerulea and B. caerulea-grandis were hybrids and (or) introgressants between B. cordifolia and B. populifolia, confirming the study by Brittain and Grant on the Grand Manan Island population in which the name × B. caerulea Blanchard was given to all individuals resulting from hybridization or backcrosses between these two taxa. Significant interlocality (Valcartier and Grand Manan Island) differences were noted for measurements of some characters: for B. papyrifera, the number of pairs of lateral veins in the leaf and guard cell length; for B. cordifolia, achene length, pairs of lateral veins in leaf, and guard cell length; for × B. caerulea, bract length and pairs of lateral veins in leaf; for B. populifolia, style length.


Sign in / Sign up

Export Citation Format

Share Document