We study methods for extracting importance scores for nodes on a directed graph, using only the topology of the graph as a guide. Such ranking has many applications in directed networks. Our strategy is to find an eigenvector, which is positive everywhere on the graph and can be in interpreted as a global importance function for its topological content, avoiding significant modification of the ...

We give a method to construct cospectral graphs for the normalized Laplacian by a local modification in some graphs with special structure. Namely, under some simple assumptions, we can replace a small bipartite graph with a cospectral mate without changing the spectrum of the entire graph. We also consider a related result for swapping out biregular bipartite graphs for the matrix A + tD. We p...

We investigate the following modification of the well known irregularity strength of graphs. Given a total weighting w of a graph G = (V,E) with elements of a set {1, 2, . . . , s}, denote wtG(v) = ∑ e3v w(e)+w(v) for each v ∈ V . The smallest s for which exists such a weighting with wtG(u) 6= wtG(v) whenever u and v are distinct vertices of G is called the total vertex irregularity strength of...

Deo and Micikevicius recently gave a new bijection for spanning trees of complete bipartite graphs. In this paper we devise a generalization of Deo and Micikevicius’s method, which is also a modification of Olah’s method for encoding the spanning trees of any complete multipartite graph K(n1, . . . , nr). We also give a bijection between the spanning trees of a planar graph and those of any of ...

Given a Euclidean graph G in Rd with n vertices and m edges, we consider the problem of adding an edge to G such that the stretch factor of the resulting graph is minimized. Currently, the fastest algorithm for computing the stretch factor of a graph with positive edge weights runs in O(nm+n2 log n) time, resulting in a trivial O(n3m+n4 log n) time algorithm for computing the optimal edge. Firs...

In this work, the study of corona domination in graphs is carried over which was initially proposed by G. Mahadevan et al. Let be a simple graph. A dominating set S graph said to corona-dominating if every vertex either pendant or support vertex. The minimum cardinality among all sets called corona-domination number and denoted (i.e) . exact value for some specific types are given. Also, result...

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

sulfur mustard (sm, bis- (2-chloroethyl) sulphide) is a chemical warfare agent that causes dna alkylation, protein modification and membrane damage. sm can trigger several molecular pathways involved in inflammation and oxidative stress, which cause cell necrosis and apoptosis, and loss of cells integrity and function. epigenetic regulation of gene expression is a growing research topic and is ...

the order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. in this paper, we study the connectivity and diameter of this  graph. also we give a relation between the order graph and prime  graph of a group.

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...