[
    {
        "id": "osp-13775",
        "type": "article-journal",
        "title": "The Conditional Fault-Diameter of the K-ary n-Cube",
        "author": [
            {
                "family": "Day",
                "given": "Khaled"
            },
            {
                "family": "Touzene",
                "given": "Abderezak"
            }
        ],
        "URL": "https://omanscience.com/en/articles/the-conditional-fault-diameter-of-the-k-ary-n-cube",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2005
                ]
            ]
        },
        "container-title": "Sultan Qaboos University Journal for Science",
        "volume": "10",
        "page": "63",
        "DOI": "10.24200/squjs.vol10iss0pp63-75",
        "publisher": "Sultan Qaboos University",
        "ISSN": "2308-3921",
        "abstract": "We obtain the conditional fault diameter of the k-ary n-cube interconnection network. It has been previously shown that under the condition of forbidden faulty sets (i.e. assuming each non-faulty node has at least one non-faulty neighbor), the k-ary n-cube, whose connectivity is 2n, can tolerate up to 4n-3 faulty nodes without becoming disconnected. We extend this result by showing that the conditional fault-diameter of the k-ary n-cube is equal to the fault-free diameter plus two. This means that if there are at most 4n-3 faulty nodes in the k-ary n-cube and if every non-faulty node has at least one non-faulty neighbor, then there exists a fault-free path of length at most the diameter plus two between any two non faulty nodes. We also show how to construct these fault-free paths. With this result the k-ary n-cube joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault diameter has been shown to be only two units over the fault-free diameter."
    }
]