Journal of Graph Theory 

About: Journal of Graph Theory is an academic journal published by Wiley. The journal publishes majorly in the area(s): Graph power & Chordal graph. It has an ISSN identifier of 0364-9024. Over the lifetime, 3424 publications have been published receiving 67290 citations. The journal is also known as: Graph theory.

The graph isomorphism disease

Abstract: The graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP-completeness. No efficient (i.e., polynomial-bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four-color conjecture which prompted Harary to rechristen it the “four-color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP-completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given.

Circulants and their connectivities

Abstract: There is diverse literature on various properties of a class of graphs known as circulants. We present a new result which answers the previously unsolved question of characterizing the connection sequence of circulants having point connectivity equal to point degree. We also develop some theorems regarding a new generalization of connectivity known as super-connectivity. In addition, we give a survey of published results pertinent to the study of connectivity of circulants.

The bandwidth problem for graphs and matrices—a survey

Abstract: The bandwidth problem for a graph G is to label its n vertices vi with distinct integers f(vi) so that the quantity max{| f(vi) − f(vi)| : (vi vj) ∈ E(G)} is minimized. The corresponding problem for a real symmetric matrix M is to find a symmetric permutation M' of M so that the quantity max{| i − j| : m'ij ≠ 0} is minimized. This survey describes all the results known to the authors as of approximately August 1981. These results include the effect on bandwidth of local operations such as refinement and contraction of graphs, bounds on bandwidth in terms of other graph invariants, the bandwidth of special classes of graphs, and approximate bandwidth algorithms for graphs and matrices. The survey concludes with a brief discussion of some problems related to bandwidth.

Knots and links in spatial graphs

Abstract: The main purpose of this paper is to show that any embedding of K7 in three-dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of K6 contains a pair of disjoint cycles which are homologically linked.

Star chromatic number

Abstract: A generalization of the chromatic number of a graph is introduced such that the colors are integers modulo n, and the colors on adjacent vertices are required to be as far apart as possible.