Search
3 articles for “Graph, vertex, edge, function, Number.”
-
On Graph Theory Based on Matrix
Abstract: This paper presents a new approach of graph theory based on natural numbers and matrix only. The natural number is used for vertex and matrix for the edge. The fast graph generation is an advantage of this approach by the successor function. The connected and non-connected graph both is defined by the axiom. There is the arithmetic based on the additive and multiplicative operation over the matrix with the set …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 1, 2022 · pp. 40–46 Read article
-
3-Equitable Labeling in Context of Ring Sum of Graphs
Abstract: A function f from vertex set V of a graph G to the set {0, 1, 2} is called 3-equitable labeling if the edge labels produced by absolute difference of the labels of end vertices of the respective edges in such a way that the number of edges with label i and j differ by atmost 1 and similarly the number of vertices with label i and j differby atmost …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 2, Issue 3, 2015 · pp. 10–19 Read article
-
Intuitionistic Fuzzy Hypergraph Laplacians and Dominating Transversals for Resilient Discrete Network Design
Abstract: This manuscript develops a discrete mathematical framework for resilience analysis on networks whose interactions are polyadic, uncertain, and partially conflicting. Classical graphs compress multi-way coordination into pairwise edges, while ordinary fuzzy graphs often ignore the non-membership information that becomes critical in emergency logistics, infrastructure interdependence, and cyberphysical coordination. We therefore formulate an intuitionistic fuzzy hypergraph in which each vertex hyperedge incidence carries membership, non-membership, and hesitation, and we construct a …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 2, 2026 · pp. 15–21 Read article