On Automorphisms of Strongly Regular Graphs

Strongly regular graphs with non-trivial automorphisms

CERTAIN TYPES OF EDGE m-POLAR FUZZY GRAPHS

In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy  sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. W...

Symplectic graphs and their automorphisms

The general symplectic graph Sp(2ν, q) is introduced. It is shown that Sp(2ν, q) is strongly regular. Its parameters are computed, its chromatic number and group of graph automorphisms are also determined.

Homomorphisms of Strongly Regular Graphs

We prove that if G and H are primitive strongly regular graphs with the same parameters and φ is a homomorphism from G to H, then φ is either an isomorphism or a coloring (homomorphism to a complete subgraph). Moreover, any such coloring is optimal for G and its image is a maximum clique of H. Therefore, the only endomorphisms of a primitive strongly regular graph are automorphisms or colorings...

On the Automorphism Groups of Strongly Regular Graphs II

We derive strong constraints on the automorphism groups of strongly regular (SR) graphs, resolving old problems motivated by Peter Cameron’s 1981 description of large primitive groups. Trivial SR graphs are the disjoint unions of cliques of equal size and their complements. Graphic SR graphs are the line-graphs of cliques and of regular bipartite cliques (complete bipartite graphs with equal pa...