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View article: Some New Results for Reverse Graph Energies and Graph Operations
Some New Results for Reverse Graph Energies and Graph Operations Open
In this paper, we establish the notions of reverse first Zagreb energy, reverse second Zagreb energy, and reverse degree square sum energy. We show how these energies behave across various graph families. Furthermore, we analyze the splitt…
View article: On the Various Energy Forms of the Join of Complete Graphs
On the Various Energy Forms of the Join of Complete Graphs Open
The concept of graph energy, first introduced in 1978, has been a focal point of extensive research within the field of graph theory, leading to the publication of numerous articles. Graph energy, originally associated with the eigenvalues…
View article: On Maximum Degree and Maximum Reverse Degree Energies of Splitting and Shadow graph of Complete graph
On Maximum Degree and Maximum Reverse Degree Energies of Splitting and Shadow graph of Complete graph Open
In this paper, the relations of maximum degree energy and maximum reserve degree energy of a complete graph after removing a vertex have been shown to be proportional to the energy of the complete graph. The results of splitting the graph …
View article: Cycles and Paths Related Vertex-Equitable Graphs
Cycles and Paths Related Vertex-Equitable Graphs Open
A vertex labeling ξ of a graph χ is referred to as a ‘vertex equitable labeling (VEq.)’ if the induced edge weights, obtained by umming the labels of the end vertices, satisfy the following condition: the absolute difference in the number …
View article: The Edge-Weighted Graph Entropy Using Redefined Zagreb Indices
The Edge-Weighted Graph Entropy Using Redefined Zagreb Indices Open
Measurements of graphs and retrieving structural information of complex networks using degree-based network entropy have become an informational theoretical concept. This terminology is extended by the concept of Shannon entropy. In this p…
View article: Study of Graphene Networks and Line Graph of Graphene Networks via <i>NM</i>‐Polynomial and Topological Indices
Study of Graphene Networks and Line Graph of Graphene Networks via <i>NM</i>‐Polynomial and Topological Indices Open
The topological invariants are related to the molecular graph of the chemical structure and are numerical numbers that help us to understand the topology of the concerned chemical structure. With the help of these numbers, many properties …
View article: Numerous graph energies of regular subdivision graph and complete graph
Numerous graph energies of regular subdivision graph and complete graph Open
The graph energy E(G) of a simple graph G is sum of its absolute eigenvalues where eigenvalues of adjacency matrix A(G) are referred as eigenvalues of graph G. Depends upon eigenvalues of different graph matrices, several graph energies ha…
View article: Distance Measurements Related to Cartesian Product of Cycles
Distance Measurements Related to Cartesian Product of Cycles Open
Graph theory and its wide applications in natural sciences and social sciences open a new era of research. Making the graph of computer networks and analyzing it with aid of graph theory are extensively studied and researched in the litera…
View article: Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights
Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights Open
The graph entropy was proposed by Körner in the year 1973 when he was studying the problem of coding in information theory. The foundation of graph entropy is in information theory, but it was demonstrated to be firmly identified with some…
View article: Redefined Zagreb indices of Rhombic, triangular, Hourglass and Jagged-rectangle benzenoid systems
Redefined Zagreb indices of Rhombic, triangular, Hourglass and Jagged-rectangle benzenoid systems Open
In the fields of mathematical chemistry and chemical graph theory, a topological index generally called a connectivity index is a kind of a molecular descriptor that is calculated in perspective of the molecular graph of a chemical compoun…
View article: Radio Labeling for Strong Product K<sub>3</sub> ⊠ P<sub>n</sub>
Radio Labeling for Strong Product K<sub>3</sub> ⊠ P<sub>n</sub> Open
Many variations of graph labeling has been defined in the literature. e.g., graceful, harmonious and radio labeling etc. In information technology and in data sciences, we need secrecy of data, different channel assignment and accuracy of …
View article: Stacked book graphs are cycle-antimagic
Stacked book graphs are cycle-antimagic Open
A family of subgraphs of a finite, simple and connected graph $G$ is called an edge covering of $G$ if every edge of graph $G$ belongs to at least one of the subgraphs. In this manuscript, we define the edge covering of a stacked book grap…
View article: Radio Number for Generalized Petersen Graphs $P(n,2)$
Radio Number for Generalized Petersen Graphs $P(n,2)$ Open
Let be a connected graph and be the distance between any two vertices of . The diameter of is denoted by and is equal to . The radio labeling (RL) for the graph is an injective function such that for any pair of vertices and . The s…
View article: On Center, Periphery and Average Eccentricity for the Convex Polytopes
On Center, Periphery and Average Eccentricity for the Convex Polytopes Open
A vertex v is a peripheral vertex in G if its eccentricity is equal to its diameter, and periphery P ( G ) is a subgraph of G induced by its peripheral vertices. Further, a vertex v in G is a central vertex if e ( v ) = r a d ( G ) , and t…
View article: RADIO LABELING AND RADIO NUMBER FOR GENERALIZED CATERPILLAR GRAPHS
RADIO LABELING AND RADIO NUMBER FOR GENERALIZED CATERPILLAR GRAPHS Open
A Radio labeling of the graph G is a function g from the vertex set V (G) of G to ℤ+ such that |g(u) - g(v)| ≥ diam(G) + 1 - dG(u, v), where diam(G) and d(u, v) are diameter and distance between u and v in graph G respectively. The radio n…
View article: Multi-level and antipodal labelings for certain classes of circulant graphs
Multi-level and antipodal labelings for certain classes of circulant graphs Open
A radio k-labeling c of a graph G is a mapping c : V (G) → Z + ∪{0} such that d(u, v)+|c(u)-c(v)| ≥ k+1 for every two distinct vertices u and v of G, where d(u, v) is the distance between any two vertices u and v of G.The span of a radio k…