Exploiting network data (i.e., graphs) is a rather particular case of data mining. The size and relevance of network domains justifies research on graph mining, but also brings forth severe complications. Computational aspects like scalability and parallelism have to be reevaluated, and well as certain aspects of the data mining process. One of those are the methodologies used to evaluate graph...

Graph databases supporting retrieval based on structural similarity utilize structure indexes. A structure index is a data structure that indexes different structural features of member graphs. These features are typically extracted at insertion time. However, as the extraction of structural features may suffer from combinatorial explosion, the structure index takes long insertion time and larg...

Abstract. In this paper we present an algorithm for drawing an undirected graph G which takes advantage of the structure of the modular decomposition tree of G. Specifically, our algorithm works by traversing the modular decomposition tree of the input graph G on n vertices and m edges, in a bottom-up fashion until it reaches the root of the tree, while at the same time intermediate drawings ar...

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.

Abstract We give an explicit positive answer, in the case of reduced curve singularities, to a question B. Teissier about existence toric embedded resolution after reembedding. In singularity ( C , O ) contained non singular surface S such reembedding may be defined terms sequence maximal contact curves minimal . prove that there exists modification, reembedding, which provides use properties s...

The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) ...

it is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (castelnuovo-mumford) regularity. as a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph g are equal provided g is well-covered bipa...

‎let $s$ be a subset of a finite group $g$‎. ‎the bi-cayley graph ${rm bcay}(g,s)$ of $g$ with respect to $s$ is an undirected graph with vertex set $gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin g‎, ‎ sin s}$‎. ‎a bi-cayley graph ${rm bcay}(g,s)$ is called a bci-graph if for any bi-cayley graph ${rm bcay}(g,t)$‎, ‎whenever ${rm bcay}(g,s)cong {rm bcay}(g,t)$ we have $t=gs^alpha$ for some $...

the concept of the bipartite divisor graph for integer subsets has been considered in [‎graph combinator., ‎ 26 (2010) 95--105‎.]. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $g...