منابع مشابه
Which trees are link graphs?
The link of a vertex v of a graph G is the subgraph induced by all vertices adjacent to U. If all the links of G are isomorphic to L, then G has constant link and L is called a link graph. We investigate the trees of order p < 9 to see which are link graphs. Group theoretic methods are used to obtain constructions of graphs G with constant link L for certain trees L. Necessary conditions are de...
متن کاملWhich graphs are pluperfect?
A graph G is pluperfect if one can add new multiple edges to obtain a multi graph M satisfying: (1) G spans M, (2) the degrees of the nodes of M are consecutive integers, (3) G and M have the same minimum degree. Our purpose is to display several families of pluperfect graphs in order to L Introduction My good friends Mehdi Behzad and Gary Chartrand wrote a note [1] titled "No graph is perfect"...
متن کاملOn graphs which contain all small trees
Communicated by the Managing Editors We investigate those graphs G, with the property that any tree on N vertices occurs as subgraph of G,. In particular, we consider the problem of estimating the minimum number of edges such a graph can have. We show that this number is bounded below and above by $z log II and nl+l/log log %, respectively. A typical question in extremal graph theory1 is one wh...
متن کاملWhich Haar graphs are Cayley graphs?
For a finite group G and subset S of G, the Haar graph H(G,S) is a bipartite regular graph, defined as a regular G-cover of a dipole with |S| parallel arcs labelled by elements of S. If G is an abelian group, then H(G,S) is well-known to be a Cayley graph; however, there are examples of non-abelian groups G and subsets S when this is not the case. In this paper we address the problem of classif...
متن کاملWhich Cayley Graphs are Integral?
Let G be a non-trivial group, S ⊆ G \ {1} and S = S−1 := {s−1 | s ∈ S}. The Cayley graph of G denoted by Γ(S : G) is a graph with vertex set G and two vertices a and b are adjacent if ab−1 ∈ S. A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine all connected cubic integral Cayley graphs. We also introduce some infinite families of connected integra...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1980
ISSN: 0095-8956
DOI: 10.1016/0095-8956(80)90085-4