Pendant 3-tree-connectivity of augmented cubes
Pages 19395 - 19413
Abstract
The Steiner tree problem in graphs is widely studied because of its usefulness in network design and circuit layout. In this context, given a set of vertices a tree that connects all vertices in S is called an S-Steiner tree. This helps to measure how well a network G can connect any set of S vertices together. In an S-Steiner tree, if each vertex in S has only one connection, it is called a pendant S-Steiner tree. Two pendant S-Steiner trees, T and are internally disjoint if and The local pendant tree-connectivity, denoted as represents the maximum number of internally disjoint pendant S-Steiner trees in graph G. For an integer k with where n is the number of vertices, the pendant k-tree-connectivity, denoted as is defined as This paper focuses on studying the pendant 3-tree-connectivity of augmented cubes, which are modified versions of hypercubes designed to enhance connectivity and reduce diameter. This research demonstrates that the pendant 3-tree-connectivity of augmented cubes, denoted as is . This result matches the upper bound of provided by Hager, specifically for the augmented cube graph .
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Publication History
Published: 27 May 2024
Accepted: 27 April 2024
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