Brick assignments and homogeneously almost self-complementary graphs

Potočnik, Primož; Šajna, Mateja

doi:10.1016/j.jctb.2008.06.002

Cited by 5 publications

(3 citation statements)

References 20 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This definition was introduced by Alspach, who also proposed the determination of all possible orders of almost self-complementary circulant graphs. In [2], this problem was solved for a particularly ''nice'' subclass of almost self-complementary circulants (called cyclically almost self-complementary), while general almost self-complementary graphs, vertex-transitive almost self-complementary graphs, and almost selfcomplementary double covers were first studied in [3], [4], and [5], respectively. Almost self-complementary graphs on one hand represent a generalization of self-complementary graphs to graphs of even order (a generalization that is particularly suitable for regular graphs) and on the other hand one of the simplest examples of index-2 isomorphic factorizations of graphs that are not complete.…”

Section: Introductionmentioning

confidence: 99%

More on almost self-complementary graphs

Francetić

Šajna

2009

Discrete Mathematics

Self Cite

View full text Add to dashboard Cite

a b s t r a c tA graph X is called almost self-complementary if it is isomorphic to one of its almost complements X c − I, where X c denotes the complement of X and I a perfect matching (1-factor) in X c . If I is a perfect matching in X c and ϕ : X → X c − I is an isomorphism, then the graph X is said to be fairly almost self-complementary if ϕ preserves I setwise, and unfairly almost self-complementary if it does not.In this paper we construct connected graphs of all possible orders that are fairly and unfairly almost self-complementary, fairly but not unfairly almost self-complementary, and unfairly but not fairly almost self-complementary, respectively, as well as regular graphs of all possible orders that are fairly and unfairly almost self-complementary.Two perfect matchings I and J in X c are said to be X -non-isomorphic if no isomorphism from X + I to X + J induces an automorphism of X . We give a constructive proof to show that there exists a graph X that is almost self-complementary with respect to two X -nonisomorphic perfect matchings for every even order greater than or equal to four.

show abstract

Section: Introductionmentioning

confidence: 99%

More on almost self-complementary graphs

Francetić

Šajna

2009

Discrete Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Various highly-symmetrical structures in this class have been intensively studied using results based on the classification of finite simple groups (see e.g. [2,4,12,15,19,22,24].…”

mentioning

confidence: 99%

Totally symmetric colored graphs

Grech

Kisielewicz

2009

Journal of Graph Theory

View full text Add to dashboard Cite

Abstract:In this paper we describe almost all edge-colored complete graphs that are fully symmetric with respect to colors and transitive on every set of edges of the same color. This generalizes the recent description of self-complementary symmetric graphs by Peisert and gives examples of permutation groups that require more than 5 colors to be represented as the automorphism group of a k-colored graph. This also contributes to the recent study of homogeneous factorizations of complete graphs. The result relies on the classification of finite simple groups.

show abstract

“…In this note we present a new result on imprimitive permutation groups of degree twice a prime that serves as a crucial tool in the classification of homogeneously almost selfcomplementary graphs of order four times a prime in [8]. We use standard terminology and notation as introduced in [9] and [8]. Theorem 1.…”

mentioning

confidence: 99%