496 research outputs found
Strong Domination Index in Fuzzy Graphs
Topological indices play a vital role in the area of graph theory and fuzzy
graph (FG) theory. It has wide applications in the areas such as chemical graph
theory, mathematical chemistry, etc. Topological indices produce a numerical
parameter associated with a graph. Numerous topological indices are studied due
to its applications in various fields. In this article a novel idea of
domination index in a FG is defined using weight of strong edges. The strong
domination degree (SDD) of a vertex u is defined using the weight of minimal
strong dominating set (MSDS) containing u. Idea of upper strong domination
number, strong irredundance number, strong upper irredundance number, strong
independent domination number, and strong independence number are explained and
illustrated subsequently. Strong domination index (SDI) of a FG is defined
using the SDD of each vertex. The concept is applied on various FGs like
complete FG, complete bipartite and r-partite FG, fuzzy tree, fuzzy cycle and
fuzzy stars. Inequalities involving the SDD and SDI are obtained. The union and
join of FG is also considered in the study. Applications for SDD of a vertex is
provided in later sections. An algorithm to obtain a MSDS containing a
particular vertex is also discussed in the article
Advances and Novel Approaches in Discrete Optimization
Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms
Discrete Mathematics and Symmetry
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group
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