Abdul Raheem

• PhD Mathematics
• Senior Lecturer at Govt Post Graduate College Asghar Mall Rawalpindi

In order to identify the basic structural properties of a network such as connectedness, centrality, modularity, accessibility, clustering, vulnerability, and robustness, we need distance-based parameters. A number of tools like these help computer and chemical scientists to resolve the issues of informational and chemical structures. In this way,...

A bijective map ρ from V(Ω) →{1,2, … |V(Ω)|} is called sum divisor cordial labeling for graph Ω so that for every uυ ∈ E(Ω) edge is fixed the label 1 if 2 divides ρ (u) + ρ(υ) and 0 otherwise, then the difference between number of edges labeled with 1 and the number of edges labeled with 0 by at most 1. A graph is called sum divisor cordial graph i...

Introduction A graph is supposed to be regular if all vertices have equal degree, otherwise irregular. Materials and Methods Polycyclic aromatic hydrocarbons are important combusting material and considered as class of carcinogens. These polycyclic aromatic hydrocarbons play an important role in graphitisation of medical science. A topological ind...

A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjastic and Gutman (1972) used molecular descriptors to find the boiling point of paraffin and total π-electron ene...

An edge-magic total (EMT) labeling for graph Γ is one-one map from π : V(Γ) ∪ E(Γ) → {1, 2, … ,|V(Γ)|+|E(Γ)|}, so that there manage a number c along a rule that for every edge, uv ∈ E(Γ), π (u) + π (uv) + π (v) = c. And if all vertices are assigned with positive integral numbers {1, 2, … ,|V(Γ)|} then this type of labeling is called a super EMT lab...

For a simple graph G, a vertex labeling : V (G) ! f1; 2; : : : ; kg is called k-labeling. The weight of an edge xy in G, denoted by w�(xy), is the sum of the labels of end vertices x and y, i.e. w (xy) = (x)+ (y). A vertex k-labeling is de ned to be an edge irregular k-labeling of the graph G if for every two di�erent edges e and f, there is w (e)...

A reverse edge magic total (REMT) labeling for the graph Γ = (V(Γ), E(Γ)) along with cardinality of p = |V(G)| and q = |E(G)| respectively. A one-one map π: V(Γ) ∪ E(Γ) → {1, 2, … ,|V(Γ)|+|E(Γ)|} having a rule that for every edge, uv ϵ E(Γ), then π (uv) − {π (u) + π (v)} = c, where c is a magic number. A reverse edge magic total (REMT) labeling is...

In this paper, we investigate the cordiality of the isomorphic copies of paths mPn . We also give sufficient condition for mPn to admit the prime cordial labeling, product cordial labeling and total product cordial labeling. Furthermore, we also determine the prime cordial labeling, product cordial labeling and total product cordial labeling for su...

Geo [J. Appl. Math. Comput, 99-117, 117, (2017)] computed exactly three degree-based topological indices of the Sudoku graphs. As an extention of this study, we prove the M-polynomial of the Sudoku graphs and obtain the mathematical expressions for various topological indices which base on the M-polynomial.

A graph \(\Gamma\) (simple, finite, undirected) with an \(\Omega\)-covering has an \((\alpha,\delta)\)-\(\Omega\)-antimagic labeling if the weights of all subgraphs \(\Omega\) of graph \(\Gamma\) constitute an arithmetic progression with the common difference \(\delta\). Such a~graph is called super \((\alpha,\delta)\)-\(\Omega\)-antimagic if \(\nu...

Graph ϒ = (V(ϒ), E(ϒ)) contain finite nodes V(ϒ) and finite edges E(ϒ). We also represent the order of the graph and size as μ = |V(ϒ)| and v = |V(ϒ)|. A graph is called (a, d)-edge magic total (EAT) labeling if there exists a bijective map φ from V(ϒ) ∪ E(ϒ) to the elements if the weight-set X = {ω(qr)|qr ∈ E(ϒ)} is arithmetic progression (A. P.)...

A numeric number which represents a complete shape of the chemical graph is said to be the topological index. In this paper, we study the 2D-lattice of three-layered single- walled Titania nanotubes (SWTNT) and investigate their M-polynomial. Mainly, we compute the certain topological indices (TI’s) which relates to degree-based by the help of this...

Sanskruti index of a graph G(V(G),E(G)) with vertex-set V(G) and edge-set E(G) is S(G)=∑uv∈E(G)(SuSvSu+Sv−2)3, where Su=∑v∈NG(u)dv. In this paper, the extremal graphs in the class of unicyclic graphs are characterized with respect to the Sanskruti index, where the considered class of unicyclic graphs contains five different large families of graphs...

Graph labeling has wide applications in the field of computer science such as coding theory, cryptography, software testing, database management systems, computer architecture and networking. The computers connected in a network can now be converted in a graph and labels assigned to the graph so formed will help to regulate bandwidth, data traffic,...

A simple graph $G=(V(G),E(G))$ admits an $H$-covering if $\forall \ e \in E(G)\ \Rightarrow\ e \in E(H')$ for some $(H' \cong H )\subseteq G$. A graph $G$ with $H$ covering is an $(a,d)$-$H$-antimagic if for bijection $f:V\cup E \to \{1,2,\dots, |V(G)|+|E(G)| \}$, the sum of labels of all the edges and vertices belong to $H'$ constitute an arithmet...

A labeling is a mapping which gives the numbers as labels to the vertices and edges of a graph. In this paper, we investigate the class of the subdivided star г ≅ G(n, n + 1, m, m + 1, 2m + 1, n5,…, np) as a super (a, d)-EAT graphs for all possible values of d, m and n.

Enomoto, Llado, Nakamigawa and Ringel (1998) defined the concept of a super (a, 0)-edge-antimagic total labeling and proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In the support of this conjecture, the present paper deals with different results on super (a, d)-edge-antimagic total labeling of subdivided stars...