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### Symmetric Y-graphs and H-graphs

J.D Horton, I.Z Bouwer
1991 Journal of combinatorial theory. Series B (Print)
SOME RESULTS COMMON TO BOTH Y-GRAPHS AND H-GRAPHS Although the techniques used to find all symmetric Y-graphs and H-graphs tend to be very specific, some results are common to both types of graphs.  ...  SYMMETRIC H-GRAPHS Not surprisingly, the techniques used with Y-graphs can also be used with H-graphs.  ...

### the Graph point – symmetric

2021 Al-Qadisiyah Journal Of Pure Science
Cayley graph has been introduced by A . Cayley , which is point – symmetric . However in this paper , I have found another type of symmetric graph , which is not Cayley graph .  ...  This graph is called peterson graph with 10 vertices is proposed  ...  (ay) ↔ ↔ (T a x , T a y ) € E C.delome gave a process to constract of graphs which is point symmetric graph , let G be any finite group H subgroup of G and A is subset of G the graph [G,H,A] which G acts  ...

### Symmetric Graphs have symmetric Matchings [article]

Jan Fricke
2016 arXiv   pre-print
Surprisingly, the reversed is also true for amenable groups: if there is a perfect matching on the graph, there is also a perfect matching on the factor graph, i. e. a group invariant ("symmetric") perfect  ...  matching on the graph.  ...  Symmetric graphs have symmetric matchings Now we can formulate and proof the main result: Let (A, B, E) a locally finite G-symmetric bipartite graph, where G is amenable.  ...

### Fibrations of graphs

Paolo Boldi, Sebastiano Vigna
2002 Discrete Mathematics
A ÿbration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods.  ...  This paper develops systematically the theory of graph ÿbrations, emphasizing in particular those results that recently found application in the theory of distributed systems.  ...  Let G and H be Schreier graphs of the same degree. Then there is a Schreier graph J ⊆ G×H covering G and H . If G and H are symmetric; ÿnite; loopless or separated; so is J . Proof.  ...

### An Upper Bound on the Size of Obstructions for Bounded Linear Rank-Width [article]

2014 arXiv   pre-print
Using the algebraic operations introduced by Courcelle and Kanté, and then extended to (skew-)symmetric matrices by Kanté and Rao, we define boundaried s-labelled graphs and prove similar structure theorems  ...  We provide a doubly exponential upper bound in p on the size of forbidden pivot-minors for symmetric or skew-symmetric matrices over a fixed finite field F of linear rank-width at most p.  ...  Two σ-symmetric F * -graphs G and H are simply isomorphic if there is a bijection h : V G → V H such that for every x and y in V G we have that M G [x, y] = M H [h(x), h(y)].  ...

### Fastest Mixing Markov Chain on Symmetric K-Partite Network [article]

2010 arXiv   pre-print
namely Symmetric K-PPDR, Semi Symmetric K-PPDR, Cycle K-PPDR and Semi Cycle K-PPDR networks.  ...  equivalent symmetric K-PPDR network and at the same time symmetric K-PPDR network has better mixing rate per step than its equivalent semi symmetric K-PPDR network at first few iterations.  ...  We denote the set of nodes on ˩-th set of symmetric H-PPDR graph by {˩ { where ˩ and vary from ŵ to H and ŵ to J respectively. Fig. 1 . 1 A symmetric H-PPDR network for H ź J ŷ.  ...

### Well-quasi-ordering of matrices under Schur complement and applications to directed graphs

2012 European journal of combinatorics (Print)
We generalise this result to σ-symmetric matrices introduced by Rao and myself in [The Rank-Width of Edge-Coloured Graphs, arXiv:0709.1433v4].  ...  In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that, for a fixed finite field F, any infinite sequence M_1,M_2,... of (skew) symmetric matrices  ...  Courcelle and the anonymous referee for their helpful comments. The author is supported by the DORSO project of ''Agence Nationale Pour la Recherche''.  ...

### Symmetric Graphs and their Quotients [article]

Robin Langer
2013 arXiv   pre-print
In this expository paper we describe a group theoretic characterization of arc-transitive graphs and their quotients.  ...  When passing from a symmetric graph to its quotient, much information is lost, but some of this information may be recovered from a certain combinatorial design on the blocks, as well as a bipartite graph  ...  For any pair of groups H ≤ G and any a ∈ G such that a ∈ H and a 2 = 1, the Sabidussi graph Sab(G, H, HaH) is G-symmetric. Furthermore every symmetric graph is of this form for some G, H and a.  ...

### Entropy of Symmetric Graphs [article]

Seyed Saeed Changiz Rezaei, Chris Godsil
2013 arXiv   pre-print
Particularly, this means that a bipartite graph is symmetric with respect to graph entropy if and only if it has a perfect matching.  ...  transitive graphs are symmetric with respect to graph entropy.  ...  Now, we show that graph G has an induced subgraph G ′ with χ f (G ′ ) = χ f (G) = χ f such that if y ∈ V P (G ′ ) and y ≥ 1 χ f , then y = 1 χ f .  ...

### Symmetric graphs and interpretations

Emo Welzl
1984 Journal of combinatorial theory. Series B (Print)
The position of symmetric graphs in this geography is investigated.  ...  The mechanism of interpretation (subgraph homomorphism, homomorphic embedding, general coloring) gives rise to a "geography" of graphs.  ...  More specifically, we ask whether every interval Y(G, H)-with a symmetric graph as a lower bound and a symmetric graph (not colorequivalent to KJ as an upper bound+ontains a symmetric graph.  ...

### The Rank-Width of Edge-Coloured Graphs

2012 Theory of Computing Systems
Clique-width is a complexity measure of directed as well as undirected graphs. Rank-width is an equivalent complexity measure for undirected graphs and has good algorithmic and structural properties.  ...  and F-bi-rank-width.  ...  Two graphs G and H are isomorphic if there exists a bijection h : V G → V H such that (x, y) ∈ E G if and only if (h(x), h(y)) ∈ E H . We call h an isomorphism between G and H.  ...

### Arc-transitive cubic abelian bi-Cayley graphs and BCI-graphs

Hiroki Koike, István Kovács
2016 Filomat
A 0-type graph can be represented as the graph BiCay(H, S), where S is a subset of H, the vertex set of which consists of two copies of H, say H 0 and H 1 , and the edge set is {{h 0 , 1 } : h, ∈ H, h  ...  A bi-Cayley graph BiCay(H, S) is called a BCI-graph if for any bi-Cayley graph BiCay(H, T), BiCay(H, S) BiCay(H, T) implies that T = hS α for some hH and α ∈ Aut(H).  ...  In this case Γ F14 (the Heawood graph), and (7) follows at once because X and R(H) are Sylow 7-subgroups of Aut(Γ).  ...

### Many symmetrically indivisible structures [article]

2014 arXiv   pre-print
Kojman and A. Onshuus in "On symmetric indivisibility of countable structures" (Cont. Math. 558(1):453--466): Let M be a symmetrically indivisible structure in a language L. Let L_0 ⊆L.  ...  Using this method, we construct 2^_0 many non-isomorphic symmetrically indivisible countable structures in given (elementary) classes and answer negatively the following question asked by A.  ...  Let G, H be graphs, for convenience assume |G| ∩ |H| = ∅. We define G + G H the graph whose universe is |G| ∪ |H| and E (G+ G H) := E G ∪ E H .  ...

### On Isomorphisms of Vertex-transitive Graphs [article]

Jing Chen, Binzhou Xia
2016 arXiv   pre-print
Some interesting vertex-transitive graphs are given, including a first example of connected symmetric non-Cayley non-GI-graph.  ...  The isomorphism problem of Cayley graphs has been well studied in the literature, such as characterizations of CI (DCI)-graphs and CI (DCI)-groups.  ...  Here a graph Γ is called G-symmetric for some G Aut(Γ) if G acts transitively on the arc set of Γ, and Γ is simply called symmetric if Γ is Aut(Γ)-symmetric.  ...

### The enumeration of bipartite graphs

Phil Hanlon
1979 Discrete Mathematics
If h =fig) then the non-symmetric, connected, bicolored graphs fall into 2-cycles, whereas the symmet-ic, connected bicoiored graphs fall into 1-cycles. Thus w2~(Y: (rg)) -G(y ~', 0), w2,.  ...  -mnbcr of connected, symmetric bicolored graphs.  ...  and so F(x, O) and F(O, y) a" ~ given by the first , ouatio::: in Theorem 1. Also G(x, y) = G(x. 0)-, G(0. y) and so to find G(£, y) it suites to find G(x,O) at, . (0, y).  ...
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