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In this monography, it is proposed to consider the concepts of spectra of edge cuts and edge cycles of a graph as a basic mathematical structure for solving the problem of graph isomorphism. An edge cut is defined by an edge and the…
A topological index reflects the physical, chemical and structural properties of a molecule, and its study has an important role in molecular topology, chemical graph theory and mathematical chemistry. It is a natural problem to…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
In this paper we study the Szeged index of partial cubes and hence generalize the result proved by V. Chepoi and S. Klav\v{z}ar, who calculated this index for benzenoid systems. It is proved that the problem of calculating the Szeged index…
Computing the diameter, and more generally, all eccentricities of an undirected graph is an important problem in algorithmic graph theory and the challenge is to identify graph classes for which their computation can be achieved in…
There are various topological indices for example distance based topological indices and degree based topological indices etc. In QSAR/QSPR study, physiochemical properties and topological indices for example atom bond connectivity index,…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that…
Let G = G(V,E) be a graph with | V | vertices and | E | edges and total graph, T(G) is obtained from G. In This paper we have study the Harmonic index of total graph for standards graphs, bipartite graph of particular type, regular graph,…
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…
The Zero divisor Graph of a commutative ring $R$, denoted by $\Gamma[R]$, is a graph whose vertices are non-zero zero divisors of R and two vertices are adjacent if their product is zero. The compressed zero divisor graph $\Gamma_E[R]$ is…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
The edge-hyper-Wiener index of a connected graph $G$ is defined as $WW_e(G) = \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f) + \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f)^2$. We develop a method for computing the…
The study of graphs associated with of various algebraic structures is an emerging topic in algebraic graph theory. Recently, the concept of nonzero component graph of a finite dimensional vector space $\Gamma(\mathbb{V})$ was put forward…
In this paper we give new bounds for a several vertex-based and edge-based topological indices of graphs: Albertson irregularity index, degree variance index, Mostar and the first Zagreb index. Moreover, we give a new upper bound for the…
We show that there exist linear-time algorithms that compute the strong chromatic index of Halin graphs, of maximal outerplanar graphs and of distance-hereditary graphs.
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…