Two graphs G and G' are said to be k-isomorphic if their edge sets can be partitioned into E(G) = ElUE2 u . . . uEk and E(G' > = E-j-U E; IJ l . . IJEk such that as graphs, E i and E! are 1 isomorphic for l<i<k. In this note we show that it is NP-complete to decide whether two graphs are 2-isomorphic. This research was supported in part by National Science Foundation grant MCS77-05313. -I * Giv...

This paper presents an exhaustive approach for verification of the weak reconstruction of Self Complementary Graphs upto 17 vertices. It describes the general problem of the Reconstruction Conjecture, explaining the complexity involved in checking deck-isomorphism between two graphs. In order to improve the computation time, various pruning techniques have been employed to reduce the number of ...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

For every integer g, isomorphism of graphs of Euler genus at most g can be decided in linear time. This improves previously known algorithms whose time complexity is nO(g) (shown in early 1980’s), and in fact, this is the first fixed-parameter tractable algorithm for the graph isomorphism problem for bounded genus graphs in terms of the Euler genus g. Our result also generalizes the seminal res...

For a given pair of pattern and data graphs, the subgraph isomorphism finding problem locates all instances graph into graph. isomorphic image in graph, set ordered pairs graph’s vertices their respective images is called an embedding. Many solvers, such as $\mathrm {Turbo_{ISO}}$ , Glasgow VF3 exist literature for problem. Though each solver aims to minimize computing costs its own way, comput...

We investigate the condition for isomorphism between circulant graphs which is known as the Ádám property. We describe a wide class of graphs for which the Ádám conjecture holds (and even in a stronger form refering to isospectrality rather than to isomorphism of graphs. In the important case of double loop (circulant graphs of degree 4) we give an almost complete classification of all possible...

The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. In this paper an efficient algorithm to generate regular graphs with given number of vertices and vertex degree is introduced. The method is based on orderly generation refined by criteria to avoid isomorphism checking and combined with a fast test for canonicity. ...

In this paper, we study the parallel and the space complexity of the graph isomorphism problem (GI) for several parameterizations. Let H = {H1,H2, · · · ,Hl} be a finite set of graphs where |V (Hi)| ≤ d for all i and for some constant d. Let G be an H-free graph class i.e., none of the graphs G ∈ G contain any H ∈ H as an induced subgraph. We show that GI parameterized by vertex deletion distan...