By combining the notions of interval-valued m-polar fuzzy graphs and graphs, notion cubic is first introduced. Then, degree a vertex in complete defined. After that, concepts direct product strong are given. Moreover, weak isomorphism co-weak defined, examples given to prove that not an isomorphism. Finally, complement presented.

Luks’s algorithm (JCSS 1982) to test isomorphism of bounded degree graphs in polynomial time is one of the most important results in the context of the Graph Isomorphism Problem and has been repeatedly used as a basic building block for many other algorithms. In particular, for graphs of logarithmic degree, Babai’s quasipolynomial isomorphism test (STOC 2016) essentially boils down to Luks’s al...

We present a novel randomized approach to the graph isomorphism problem. Our algorithm aims at solving difficult instances by producing randomized certificates for non-isomorphism. We compare our implementation to the de facto standard nauty. On many of the hardest known instances, the incidence graphs of finite projective planes, our program is considerably faster than nauty. However, it is in...

The d-measurement set of a graph is its set of possible squared edge lengths over all d-dimensional embeddings. In this note, we define a new notion of graph isomorphism called d-measurement isomorphism. Two graphs are d-measurement isomorphic if there is agreement in their d-measurement sets. A natural question to ask is “what can be said about two graphs that are d-measurement isomorphic?” In...

Kwak, J.H. and J. Lee, Isomorphism classes of cycle permutation graphs, Discrete Mathematics 105 (1992) 131-142. In this paper, we construct a cycle permutation graph as a covering graph over the dumbbell graph, and give a new characterization of when two given cycle permutation graphs are isomorphic by a positive or a negative natural isomorphism. Also, we count the isomorphism classes of cycl...

The group isomorphism problem consists in deciding whether two groups G and H given by their multiplication tables are isomorphic. An algorithm for group isomorphism attributed to Tarjan runs in time n, c.f. [Mil78]. Miller and Monk showed in [Mil79] that group isomorphism can be many-one reduced to isomorphism testing for directed graphs. For groups with n elements, the graphs have valence at ...

This paper deals with the graph isomorphism (GI) problem for two graph classes: chordal bipartite graphs and strongly chordal graphs. It is known that GI problem is GI complete even for some special graph classes including regular graphs, bipartite graphs, chordal graphs, comparability graphs, split graphs, and k-trees with unbounded k. On the other side, the relative complexity of the GI probl...

The questions of isomorphism degree estimation of fuzzy graphs are discussed in this paper. The definition of independent fuzzy set of fuzzy graph is presented. The estimation method of isomorphism degree of fuzzy graphs is suggested and proved. The example of isomorphism degree estimation is considered.