The concepts of separation index of a graph and of a surface are introduced. We prove that the separation index of the sphere is 3. Also the separation index of any graph faithfully embedded in a surface of genus g is bounded by a funtion of g. 2002 Wiley Periodicals, Inc. J Graph Theory 41: 53–61, 2002 1. GRAPH ISOMORPHISM This first section on the Graph Isomorphism Problem is meant only as mo...

RDF, graph isomorphism, equality The Resource Description Framework (RDF) describes graphs of statements about resources. This paper explores the equality of two RDF graphs in light of the graph isomorphism literature. We consider anonymous resources as unlabelled vertices in a graph, and show that the standard graph isomorphism algorithms, developed in the 1970's, can be used effectively for c...

We extend the concept of graph isomorphisms to multilayer networks, and we identify multiple types of isomorphisms. For example, in multilayer networks with a single “aspect” (i.e., type of layering), permuting vertex labels, layer labels, and both of types of layers each yield a different type of isomorphism. We discuss how multilayer network isomorphisms naturally lead to defining isomorphism...

We show that the graph isomorphism problem is determined in a polynomial time. This is done by showing that that two graphs on n vertices are isomorphic if and only if a corresponding system of (4n− 1)n equations in n nonnegative variables is solvable. 2000 Mathematics Subject Classification: 03D15, 05C50, 05C60, 15A48, 15A51, 15A69, 90C05.

Abstract. A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs (i .e. all but o(2 (2 >) of the 2 t 1 graphs on n vertices) . Hence, for almost all graphs X, any graph Y can be easily tested for isomorphism to X by an extremely naive linear time algorithm . This result is based on the following : In almost all graphs on n vertices, the largest n 0 .15...

We study optimization versions of Graph Isomorphism. Given two graphs G1, G2, we are interested in finding a bijection π from V (G1) to V (G2) that maximizes the number of matches (edges mapped to edges or non-edges mapped to non-edges). We give an n time approximation scheme that for any constant factor α < 1, computes an α-approximation. We prove this by combining the n time additive error ap...

The graph isomorphism problem can be easily stated: check to see if two graphs that look di erently are actually the same. The problem occupies a rare position in the world of complexity theory, it is clearly in NP but is not known to be in P and it is not known to be NP-complete. Many sub-disciplines of mathematics, such as topology theory and group theory, can be brought to bear on the proble...

Neutrosophic theory has many applications in graph theory, interval valued neutrosophic graph (IVNG) is the generalization of fuzzy graph, intuitionistic fuzzy graph and single valued neutrosophic graph. In this paper, we introduced some types of IVNGs, which are subdivision IVNGs, middle IVNGs, total IVNGs and interval valued neutrosophic line graphs (IVNLGs), also discussed the isomorphism, c...

Several isomorphism classes of graph coverings of a graph G have been enumerated by many authors. Kwak and Lee (Canad. J. Math. XLII (1990) 747) enumerated the isomorphism classes of graph bundles and those of n-fold coverings with respect to a group of automorphisms of the base graph G which 9x a spanning tree. Hofmeister (Discrete Math. 98 (1991) 175) independently enumerated the isomorphism ...