The Martin polynomial of an oriented Eulerian graph encodes information about families of cycles in the graph. This paper uses a transformation of the Martin polynomial that facilitates standard combinatorial manipulations. These manipulations result in several new identities for the Martin polynomial, including a di.erentiation formula. These identities are then applied to get new combinatoria...

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.

Let Γ be a distance-regular graph with diameter d and Kneser graph K = Γd, the distance-d graph of Γ. We say that Γ is partially antipodal when K has fewer distinct eigenvalues than Γ. In particular, this is the case of antipodal distance-regular graphs (K with only two distinct eigenvalues), and the so-called half-antipodal distance-regular graphs (K with only one negative eigenvalue). We prov...

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.

We present a characterization of Eulerian graphs that have a k-arc-connected orientation so that the deletion of any vertex results in a (k− 1)-arc-connected directed graph. This provides an affirmative answer for a conjecture of Frank [2]. The special case, when k = 2, describes Eulerian graphs admitting 2-vertexconnected orientations. This case was proved earlier by Berg and Jordán [1]. These...

A regular nonempty graph Γ is called edge regular, whenever there exists a nonegative integer λΓ, such that any two adjacent vertices of Γ have precisely λΓ common neighbours. An edge regular graph Γ with at least one pair of vertices at distance 2 is called amply regular, whenever there exists a nonegative integer μΓ, such that any two vertices at distance 2 have precisely μΓ common neighbours...

in this paper we study the coprime graph of a group $g$. the coprime graph of a group $g$, is a graph whose vertices are elements of $g$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. in this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. also we study the automorphism group of the coprime graph.

This thesis investigates a pragmatic approach to typing, static analysis and static optimization of Web query languages, in special the Web query language Xcerpt[43]. The approach is pragmatic in the sense, that no restriction on the types are made for decidability or efficiency reasons, instead precision is given up if necessary. Pragmatics on the dynamic side means to use types not only to en...

Let G = (V, A) be an Eulerian directed graph with an arclabeling. In this work we study the problem of finding an Eulerian circuit of lexicographically minimal label among all Eulerian circuits of the graph. We prove that this problem is NP-hard by showing a reduction from the Directed-Hamiltonian-Circuit problem. If the labeling of the arcs is such that arcs going out from the same vertex have...