Displaying similar documents to “On cyclically embeddable graphs”

On cyclically embeddable (n,n)-graphs

Agnieszka Görlich, Monika Pilśniak, Mariusz Woźniak (2003)

Discussiones Mathematicae Graph Theory

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An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider the embeddable (n,n)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.

Placing bipartite graphs of small size II

Beata Orchel (1996)

Discussiones Mathematicae Graph Theory

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In this paper we give all pairs of non mutually placeable (p,q)-bipartite graphs G and H such that 2 ≤ p ≤ q, e(H) ≤ p and e(G)+e(H) ≤ 2p+q-1.

A note on uniquely embeddable graphs

Mariusz Woźniak (1998)

Discussiones Mathematicae Graph Theory

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Let G be a simple graph of order n and size e(G). It is well known that if e(G) ≤ n-2, then there is an embedding G into its complement [G̅]. In this note, we consider a problem concerning the uniqueness of such an embedding.

Domination, independence and irredundance in graphs

Jerzy Topp

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CONTENTS1. Introduction........................................................................................................ 5 1.1. Purpose and scope................................................................................. 5 1.2. Basic graphtheoretical terms................................................................ 62. Domination, independence and irredundance in graphs................................ 9 2.1. Introduction and preliminaries.................................................................

Edge-Transitivity of Cayley Graphs Generated by Transpositions

Ashwin Ganesan (2016)

Discussiones Mathematicae Graph Theory

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Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also proved that the transposition graph T(S) is edge-transitive if and only if the Cayley graph Cay(Sn,...

The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic

Yi Wang, Yi-Zheng Fan, Xiao-Xin Li, Fei-Fei Zhang (2015)

Discussiones Mathematicae Graph Theory

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A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and...