A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P,D, gyroid and H surfaces. Some of these graphs are natural ge...

Chemical compounds and drugs are often modelled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, by virtue of mathematical derivation, we determine the fourth, f...

The Wiener index is one of the oldest graph parameter which is used to study molecular-graph-based structure. This parameter was first proposed by Harold Wiener in 1947 to determining the boiling point of paraffin. The Wiener index of a molecular graph measures the compactness of the underlying molecule. This parameter is wide studied area for molecular chemistry. It is used to study the physio...

Integrating data involving chemical structures is simplified when unique identifiers (UIDs) can be associated with chemical structures. For example, these identifiers can be used as database keys. One common approach is to use the Unique SMILES notation introduced in [2]. The Unique SMILES views a chemical structure as a graph with atoms as nodes and bonds as edges and uses a depth first traver...

Chemical compounds and drugs are often modeled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, we determine the logarithm multiplicative Wiener index and recipr...

Domination is an ancient graph theoretical topic with applications in psychology, political sci- ence, and human behaviour. A topological index area of theory that governs a compound’s molecular structure. This work aims to conglomerate the two different branches determine dominational variants some celebrated degree based index. The newly described descriptors are generalised standard graphs, ...

let g be a (p, q) graph. let f : v (g) → {1, 2, . . . , k} be a map. for each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of g if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

recently, e. m'{a}v{c}ajov'{a} and m. v{s}koviera proved that every bidirected eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. this result shows the validity of bouchet's nowhere zero conjecture for eulerian bidirected graphs. in this paper we prove the same theorem in a different terminology and with a short and simple proof. more precisely, we p...

in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...