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Supplemental material for Building a predictive soft armor finite element model combining experiments, simulations, and machine learning by Tanu Pittie, Kartikeya Kartikeya, Naresh Bhatnagar, NMA Krishnan, Thilak Senthil and Subramaniam D Rajan in Journal of Composite Materials

The concept of network is predominantly used in several applications of computer communication networks. It is also a fact that the dominating set acts as a virtual backbone in a communication network. These networks are vulnerable to breakdown due to various causes, including traffic congestion. In such an environment, it is necessary to regulate the traffic so that these vulnerabilities could be reasonably controlled. Motivated by this, [Formula: see text]-part degree restricted domination is defined as follows. For a positive integer [Formula: see text], a dominating set [Formula: see text] of a graph [Formula: see text] is said to be a [Formula: see text]-part degree restricted dominating set ([Formula: see text]-DRD set) if for all [Formula: see text], there exists a set [Formula: see text] such that [Formula: see text] and [Formula: see text]. The minimum cardinality of a [Formula: see text]-DRD set of a graph [Formula: see text] is called the [Formula: see text]-part degree restricted domination number of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we present a polynomial time reduction that proves the NP -completeness of the [Formula: see text]-part degree restricted domination problem for bipartite graphs, chordal graphs, undirected path graphs, chordal bipartite graphs, circle graphs, planar graphs and split graphs. We propose a polynomial time algorithm to compute a minimum [Formula: see text]-DRD set of a tree and minimal [Formula: see text]-DRD set of a graph.

In this paper, we propose a new multi-parameter weight based double star embedded clustering algorithm for MANETs. The weight of a node is a linear combination of six different graph theoretic parameters which deal with the communication capability of a node both in terms of quality and quantity, the relative closeness relationship between a node and the other nodes in the network, the maximum number of hops a node has to take in order to communicate with the other nodes. This paper deals with the description of the algorithm and an analysis of the algorithm in situations which lead to topology changes.

In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile Ad hoc networks. The algorithm generates double star embedded non-overlapping cluster structures, where each cluster is managed by a leader node and a substitute for the leader node (in case of failure of leader node). The weight of a node is a linear combination of six different graph theoretic parameters which deal with the communication capability of a node both in terms of quality and quantity, the relative closeness relationship between network nodes and the maximum and average distance traversed by a node for effective communication. This paper deals with the design and analysis of the algorithm and some of the graph theoretic/structural properties of the clusters obtained are also discussed.

In this paper, we propose a new distributed weighted clustering algorithm for MANETs by introducing a new graph parameter called strong degree defined based on the quality of neighbors of a node. The proposed algorithm is a cluster-head based algorithm. The parameters are so chosen to ensure high connectivity, cluster stability and energy efficient communication among nodes of high dynamic nature. This paper deals with the design and complexity analysis of the algorithm and we discuss the different cases which cause topology change and the behavior of our algorithm in these cases.