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 graph energy is a graph--spectrum--based quantity‎, ‎introduced in the 1970s‎. ‎After a latent period of 20--30 years‎, ‎it became a popular topic of research both‎ ‎in mathematical chemistry and in ``pure'' spectral graph theory‎, ‎resulting in‎ ‎over 600 published papers‎. ‎Eventually‎, ‎scores of different graph energies have‎ ‎been conceived‎. ‎In this article we...

Technology affordances are a method for technology users to carry out actions based on the possibilities provided by certain technology. In order systematically grasp research hotspots and evolution of at home abroad, clarify characteristics development direction in China, we use CiteSpace software visualize analyze literature abroad. The results abroad increasing, number scholars who have rese...

Roots of graph polynomials such as the characteristic polynomial, the chromatic polynomial, the matching polynomial, and many others are widely studied. In this paper we examine to what extent the location of these roots refl ects the graph theoretic properties of the underlying graph. (Joint work with E. Ravve and N. Blanchard) Johann (János) A. Makowsky is a Hungarian born and naturalized Swi...

Assuming P<GI<NP, the creation and verification of a digital signature of an arbitrary RDF graph cannot be done in polynomial time. However, it is possible to define a large class of canonicalizable RDF graphs, such that digital signatures for graphs in this class can be created and verified in O(nlog(n)). Without changing its meaning, an arbitrary RDF graph can be nondeterministically pre-cano...

Generic editing of visual languages can become easier with a common exchange format for graph transformation based on XML. In this sense, many XML languages (such as GXL, XGMML and GraphML) were developed to represent visual languages as a graph. These languages are compatible with XML technology and are interoperable with a great number of state of the art documentation and graphic technologie...

the tenacity of a graph g, t(g), is dened by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we dene τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph&apos;s...

let $g=(v,e)$ be a simple graph. a set $ssubseteq v$ isindependent set of $g$,  if no two vertices of $s$ are adjacent.the  independence number $alpha(g)$ is the size of a maximumindependent set in the graph. in this paper we study and characterize the independent sets ofthe zero-divisor graph $gamma(r)$ and ideal-based zero-divisor graph $gamma_i(r)$of a commutative ring $r$.

For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ED}$ graph) if $G$ has no efficient dominating set (EDS) but every graph formed by removing a single vertex from $G$ has at least one EDS, and (ii) a hypo-unique domination graph (a hypo-$mathcal{UD}$ graph) if $G$ has at least two minimum dominating sets...

In this paper, the composite order Cayley graph Cay(G, S) is introduced, where G is a group and S is the set of all composite order elements of G. Some graph parameters such as diameter, girth, clique number, independence number, vertex chromatic number and domination number are calculated for the composite order Cayley graph of some certain groups. Moreover, the planarity of composite order Ca...