A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

A recent topic in probabilistic network learning is to exploit local network structure, i.e. to capture regularities in the conditional probability distributions, and to learn networks with local structure from data. In this paper we apply this idea to possibilistic networks, i.e. we try to capture regularities in conditional possibility distributions, and present a modification of the learning...

In this paper we discuss which properties of a formally verified component are preserved when the component is changed due to an adaption to a new use. More specifically, we will investigate when a temporal logic property of an Object-Z class is preserved under a modification or extension of the class with new features. To this end, we use the slicing technique from program analysis which provi...

It is known that the expansion property of a graph influences the performance of the corresponding code when decoded using iterative algorithms. Certain graph products may be used to obtain larger expander graphs from smaller ones. In particular, the zig-zag product and replacement product may be used to construct infinite families of constant degree expander graphs. This paper investigates the...

We present a new algorithm for community detection. The algorithm uses random walks to embed the graph in a space of measures, after which a modification of k-means in that space is applied. The algorithm is therefore fast and easily parallelizable. We evaluate the algorithm on standard random graph benchmarks, including some overlapping community benchmarks, and find its performance to be bett...

In its original form, the two-graph method allows only circuit components that are described by a v-i relationship of the admittance type (G, C, gm). In particular, it excludes resistors (expressed as resistance R rather ten conductance G), inductors and current-controlled current sources. Practising circuit designers often prefer to have symbolic analysis results expressed in terms of resistan...

let $r$ be a ring with unity. the undirected nilpotent graph of $r$, denoted by $gamma_n(r)$, is a graph with vertex set ~$z_n(r)^* = {0neq x in r | xy in n(r) for some y in r^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in n(r)$, or equivalently, $yx in n(r)$, where $n(r)$ denoted the nilpotent elements of $r$. recently, it has been proved that if $r$ is a left ar...