Self-complementary Tetracationic Cyclophanes Containing 4,4′-Bipyridinium and 2,5-Dimethoxy-1,4-xylyl Subunits

4,4′-Bipyridinium-based tetracationic cyclophanes containing a 2,5-dimethoxy-1,4-xylyl unit were synthesized by using either m-terphenyl building blocks or incorporating a 4-hydroxy benzyl spacer between the complementary subunits. The cyclophanes show weak intramolecular charge-transfer (CT) bands in the visible region and one of the cyclophanes formed a green-coloured CT complex with ferrocene with an association constant (K _a) of 6.3?M^?1. The electrochemical parameters obtained for the cyclophanes indicate that all the redox processes are reversible.     

On separable self-complementary graphs

In this paper, we describe the structure of separable self-complementary graphs.     

Self-complementary Cayley Graphs of Extraspecial p-groups

This paper constructs several families of self-complementary Cayley graphs of extraspecial p-groups, where p is a prime and congruent to 1 modulo 4.     

Two-geodesic-transitive graphs which are locally self-complementary

A 2-geodesic of a graph is a vertex triple $(u,v,w)$ with v adjacent to both u and w, $u\ne w$ and $u,w$ are not adjacent. A graph is said to be 2-geodesic-transitive if its automorphism group is transitive on both the set of arcs and the set of 2-geodesics. In this paper, we first determine the family of 2-geodesic-transitive graphs which are locally self-complementary, and then classify the family of 2-geodesic-transitive graphs that the local subgraph induced by the neighbor of a vertex is an arc-transitive circulant.     

完全超紧图

Chia G.L.和Lim C.K.在东南亚第一次图论会议(1983,新加坡)文集的末尾提出六个未解决问题.第五个问题是:设H是自补图,问是否存在自补完全超紧图G,使G~*=H.第六个问题是:设G是完全超紧图.如果G_0与(?)同构,问G是否自补图.本文肯定地回答了第五个问题和否定地回答了第六个问题.     

On the forbidden induced subgraph sandwich problem

We consider the sandwich problem, a generalization of the recognition problem introduced by Golumbic et al. (1995) [15], with respect to classes of graphs defined by excluding induced subgraphs. We prove that the sandwich problem corresponding to excluding a chordless cycle of fixed length k is NP-complete. We prove that the sandwich problem corresponding to excluding K_r?e for fixed r is polynomial. We prove that the sandwich problem corresponding to 3PC(⋅,⋅)-free graphs is NP-complete. These complexity results are related to the classification of a long-standing open problem: the sandwich problem corresponding to perfect graphs.