Diameter Two Graphs of Minimum Order with Given Degree Set
Authors
Abstract:
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for a given set of natural numbers greater than one, we determine the minimum order of a 2-self-centered graph with that degree set.
similar resources
diameter two graphs of minimum order with given degree set
the degree set of a graph is the set of its degrees. kapoor et al. [degree sets for graphs, fund. math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. furthermore, the minimum order of such a graph is determined. a graph is 2-self- centered if its radius and diameter are two. in this paper for ...
full textLarge graphs of diameter two and given degree
Let r(d, 2), C(d, 2), and AC(d, 2) be the largest order of a regular graph, a Cayley graph, and a Cayley graph of an Abelian group, respectively, of diameter 2 and degree d. The best currently known lower bounds on these parameters are r(d, 2) ≥ d2 − d + 1 for d − 1 an odd prime power (with a similar result for powers of two), C(d, 2) ≥ (d+ 1)2/2 for degrees d = 2q − 1 where q is an odd prime p...
full textOn Large Graphs with Given Degree and Diameter
The degree/diameter problem is to determine the largest possible number of vertices in a graph of given maximum degree and given diameter. It is well known that the general upper bound, called Moore bound, for the order of such graphs is attainable only for certain special values of degree and diameter. Finding better upper bounds for the maximum possible number of vertices, given the other two...
full textNew Large Graphs with Given Degree and Diameter
In this paper we give graphs with the largest known order for a given degree ∆ and diameter D. The graphs are constructed from Moore bipartite graphs by replacement of some vertices by adequate structures. The paper also contains the latest version of the (∆, D) table for graphs.
full textNew large graphs with given degree and diameter six
In this paper, a method for obtaining large diameter 6 graphs by replacing some vertices of a Moore bipartite diameter 6 graph with complete Kh graphs is proposed. These complete graphs are joined to each other and to the remaining nonmodified graphs by means of new edges and by using a special diameter 2 graph. The degree of the graph so constructed coincides with the original one. © 1999 John...
full textOn Independent Domination Number of Graphs with given Minimum Degree
We prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that by J. Haviland 3] and settles Case = 2 of the corresponding conjecture by O. Favaron 2].
full textMy Resources
Journal title
volume 1 issue 2
pages 317- 323
publication date 2016-07-01
By following a journal you will be notified via email when a new issue of this journal is published.
Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023