in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner 2-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency.

A new generalization of Fiedler's lemma is obtained by introducing the concept main function a matrix. As applications, universal spectra H-join any graphs (possibly non-regular) and adjacency H-generalized join constrained (arbitrary) vertex subsets are obtained. The generalized corona deduced from graphs. Also, construction infinitely many pairs non-regular cospectral provided.

The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is introduced which is very simple and easy to implement, but very efficient in discriminating non-isomorphic graphs, in practice. This method does not need any ...