the first zagreb index $m_1$ of a graph $g$ is equal to the sum of squaresof degrees of the vertices of $g$. goubko proved that for trees with $n_1$pendent vertices, $m_1 geq 9,n_1-16$. we show how this result can beextended to hold for any connected graph with cyclomatic number $gamma geq 0$.in addition, graphs with $n$ vertices, $n_1$ pendent vertices, cyclomaticnumber $gamma$, and minimal $m...

Given a real-analytic manifold M, a compact connected Lie group G and a principal G-bundle P ! M, there is a canonicaìgeneralized measure' on the space A=G of smooth connections on P modulo gauge transformations. This allows one to deene a Hilbert space L 2 (A=G). Here we construct a set of vectors spanning L 2 (A=G). These vectors are described in terms of`spin networks': graphs embedded in M,...

We begin the study of distinguishing geometric graphs. Let G be a geometric graph. An automorphism of the underlying graph that preserves both crossings and noncrossings is called a geometric automorphism. A labelling, f : V (G) → {1, 2, . . . , r}, is said to be rdistinguishing if no nontrivial geometric automorphism preserves the labels. The distinguishing number of G is the minimum r such th...

Data science is a very visual field of computer where everything needs to be depicted graphically in order derive new forms data and conclusions from it. This paper introduces visualization techniques graphs can better rendered using advance such as vertex edge clipping against the view port, rendering large drawing area by panning port focus on specific region, labelling with numeric , text im...

the total version of geometric–arithmetic index of graphs is introduced based on the endvertexdegrees of edges of their total graphs. in this paper, beside of computing the total gaindex for some graphs, its some properties especially lower and upper bounds are obtained.

We investigate the existence of edge-magic labellings of countably infinite graphs by abelian groups. We show for that for a large class of abelian groups, including the integers Z, there is such a labelling whenever the graph has an infinite set of disjoint edges. A graph without an infinite set of disjoint edges must be some subgraph of H + I, where H is some finite graph and I is a countable...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

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.

background: chlamydia trachomatis is considered as an important cause of preventable sexually transmitted diseases worldwide. it is known to be of an obligate intracellular nature and enters its target cells via an endocytic process. as major outer membrane protein (momp) is one of the main candidates for the attachment and entry of chlamydia to the host cells we have tried to label the epitope...

the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...