Search results for "Distance-regular graph"
showing 6 items of 6 documents
Incomplete vertices in the prime graph on conjugacy class sizes of finite groups
2013
Abstract Given a finite group G, consider the prime graph built on the set of conjugacy class sizes of G. Denoting by π 0 the set of vertices of this graph that are not adjacent to at least one other vertex, we show that the Hall π 0 -subgroups of G (which do exist) are metabelian.
Partially Square Graphs, Hamiltonicity and Circumference II
2000
Abstract Given a graph G, its partially square graph G∗ is a graph obtained by adding an edge uv for each pair u, v of vertices of G at distance 2 whenever the vertices u and v have a common neighbor x satisfying the condition NG(x) ⊆ NG[u] ∪ NG[v], where NG[x]= NG(x) ∪ {x}. In case G is a claw-free graph, G∗ is equal to G2, We define σ ∗ t = min{ ∑ x∈ d ∗ G (x): S is an independent set in G ∗ and ∣S∣ = t} , where d ∗ G (x) = ∣{y ∈ V∣ xy ∈ E(G∗)}∣ . We give for hamiltonicity and circumference new sufficient conditions depending on and we improve some known results.
On the Soluble Graph of a Finite Simple Group
2013
The maximal independent sets of the soluble graph of a finite simple group G are studied and their independence number is determined. In particular, it is shown that this graph in many cases has an independent set with three vertices.
A dual of 4-regular graph forG × C2n
2003
Abstract A graph is said h-decomposable if its edge-set is decomposable into edge-disjoint hamiltonian cycles. Jha [3] conjectured that if G is a non-bipartite h-decomposable graph on even number of vertices, then G × K2 is h-decomposable. We use the notion of dual graph defined in [4], we prove that if G = Q1,2 ⊕ C3,4 is a 4-regular non-bipartite h-decomposable graph and the dual graphs relative to Q1,2 and C3,4 are connected then G × K 2 and G × C 2n are h-decomposable (where C 2n is an even cycle).
Homeomorphic graph manifolds: A contribution to the μ constant problem
1999
Abstract We give a characterization, in terms of homological data in covering spaces, of those maps between (3-dimensional) graph manifolds which are homotopic to homeomorphisms. As an application we give a condition on a cobordism between graph manifolds that guarantees that they are homeomorphic. This in turn is applied to give a partial result on the μ -constant problem in (complex) dimension three.
Optimal Mass Transport on Metric Graphs
2015
We study an optimal mass transport problem between two equal masses on a metric graph where the cost is given by the distance in the graph. To solve this problem we find a Kantorovich potential as the limit of $p$-Laplacian--type problems in the graph where at the vertices we impose zero total flux boundary conditions. In addition, the approximation procedure allows us to find a transport density that encodes how much mass has to be transported through a given point in the graph, and also provides a simple formula of convex optimization for the total cost.