In this paper, we introduce the notion of Pythagorean Anti fuzzy graph. We then define Cartesian product and Lexicographic on It is proved that two graphs graph general, lexicographic regular need not be Necessary sufficient conditions for to are determined. Further, concept isomorphism with suitable example.

In this paper, we begin the determination of all primitive strongly regular graphs with chromatic number equal to 5. Using eigenvalue techniques, we show that there are at most 43 possible parameter sets for such a graph. For each parameter set, we must decide which strongly regular graphs, if any, possessing the set are 5-chromatic. In this way, we deal completely with 34 of these parameter se...

The study of distance-regular directed graphs can be reduced to that of short distance-regular directed graphs. We consider the eigenspaces of the intersection matrix of a short distance-regular directed graph and show that nearly all the eigenvalues are nonreal. Next we show that a nontrivial short distance-regular directed graph is primitive.

We analyze when the Moore–Penrose inverse of the combinatorial Laplacian of a distance– regular graph is a M–matrix; that is, it has non–positive off–diagonal elements. In particular, our results include some previously known results on strongly regular graphs.