In [3] Cameron et al. classified strongly regular graphs with strongly regular subconstituents. Here we prove a theorem which implies that distance-regular graphs with strongly regular subconstituents are precisely the Taylor graphs and graphs with a1 = 0 and ai ∈ {0, 1} for i = 2, . . . , d .

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

let $g$ be an $(n,m)$-graph. we say that $g$ has property $(ast)$if for every pair of its adjacent vertices $x$ and $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis insensitive of any other...

We consider the (Ihara) zeta functions of line graphs, middle graphs and total graphs of a regular graph and their (regular or irregular) covering graphs. Let L(G), M(G) and T (G) denote the line, middle and total graph of G, respectively. We show that the line, middle and total graph of a (regular and irregular, respectively) covering of a graph G is a (regular and irregular, respectively) cov...

A multicone graph is defined to be join of a clique and a regular graph. A graph $ G $ is cospectral with graph $ H $ if their adjacency matrices have the same eigenvalues. A graph $ G $ is said to be determined by its spectrum or DS for short, if for any graph $ H $ with $ Spec(G)=Spec(H)$, we conclude that $ G $ is isomorphic to $ H $. In this paper, we present new classes of multicone graphs...

In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the ...

the k-th semi total point graph of a graph g, , ‎is a graph‎ obtained from g by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎in this paper‎, a formula for laplacian polynomial of in terms of‎ characteristic and laplacian polynomials of g is computed‎, ‎where is a connected regular graph‎.the kirchhoff index of is also computed‎.

Distributions over strings and trees can be represented by probabilistic regular languages, which characterise many models in natural language processing. Recently, several datasets have become available which represent natural language phenomena as graphs, so it is natural to ask whether there is an equivalent of probabilistic regular languages for graphs. This paper presents regular graph lan...