Displaying similar documents to “Universality in Graph Properties with Degree Restrictions”

Supermagic Graphs Having a Saturated Vertex

Jaroslav Ivančo, Tatiana Polláková (2014)

Discussiones Mathematicae Graph Theory

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A graph is called supermagic if it admits a labeling of the edges by pairwise different consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we establish some conditions for graphs with a saturated vertex to be supermagic. Inter alia we show that complete multipartite graphs K1,n,n and K1,2,...,2 are supermagic.

Universality for and in Induced-Hereditary Graph Properties

Izak Broere, Johannes Heidema (2013)

Discussiones Mathematicae Graph Theory

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The well-known Rado graph R is universal in the set of all countable graphs I, since every countable graph is an induced subgraph of R. We study universality in I and, using R, show the existence of 2 א0 pairwise non-isomorphic graphs which are universal in I and denumerably many other universal graphs in I with prescribed attributes. Then we contrast universality for and universality in induced-hereditary properties of graphs and show that the overwhelming majority of induced-hereditary...

Characterizations of the Family of All Generalized Line Graphs-Finite and Infinite-and Classification of the Family of All Graphs Whose Least Eigenvalues ≥ −2

Gurusamy Rengasamy Vijayakumar (2013)

Discussiones Mathematicae Graph Theory

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The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. In [P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, Line graphs, root systems, and elliptic geometry, J. Algebra 43 (1976) 305-327], the class of all finite graphs whose least eigenvalues ≥ −2 has been classified: (1) If a (finite) graph is connected and its least eigenvalue is at least −2, then either it is a generalized line graph or it is represented...

The niche graphs of interval orders

Jeongmi Park, Yoshio Sano (2014)

Discussiones Mathematicae Graph Theory

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The niche graph of a digraph D is the (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if N+D(x) ∩ N+D(y) ≠ ∅ or N−D(x) ∩ N−D(y) ≠ ∅, where N+D(x) (resp. N−D(x)) is the set of out-neighbors (resp. in-neighbors) of x in D. A digraph D = (V,A) is called a semiorder (or a unit interval order ) if there exist a real-valued function f : V → R on the set V and a positive real number δ ∈ R such that (x, y) ∈ A if...