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关于路径、完全图和完全二分图的某些构造的无线电数的进一步结果。

Further results on the radio number for some construction of the path, complete, and complete bipartite graphs.

作者信息

Mari Baskar, Jeyaraj Ravi Sankar

机构信息

Department of Mathematics, Vellore Institute of Technology, Vellore, India.

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India.

出版信息

Heliyon. 2024 Jul 14;10(14):e34434. doi: 10.1016/j.heliyon.2024.e34434. eCollection 2024 Jul 30.

DOI:10.1016/j.heliyon.2024.e34434
PMID:39130467
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11315197/
Abstract

Let be a connected graph with . Then indicates the distance of and in . For any pair of distinct vertices of , mapping from such that . The maximum label assigned to any vertex of under a radio labeling is known as the span of . The radio number of is defined as the minimum span among all possible radio labelings of . This paper aims to determine the radio number for specific constructed families of graphs with diameter 3, such as , , , , and .

摘要

设 是一个连通图，且 。那么 表示 和 在 中的距离。对于 中任意一对不同的顶点 ，从 到 的映射满足 。在一个无线电标号 下分配给 中任意顶点的最大标号称为 的跨度。 的无线电数 被定义为 的所有可能无线电标号中的最小跨度。本文旨在确定直径为3的特定构造的图族的无线电数 ，例如 、 、 、 和 。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/c05ca795f1ee/gr010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/7c2da8595d63/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/47679f49f2e6/gr002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/7731a1d4b8cd/gr003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/09e4e3c2b17f/gr004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/e16cc85665a9/gr005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/a7f7a14a765b/gr006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/b09f9d7b5eb1/gr007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/dc94767dfeca/gr008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/066863ba2047/gr009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/c05ca795f1ee/gr010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/7c2da8595d63/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/47679f49f2e6/gr002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/7731a1d4b8cd/gr003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/09e4e3c2b17f/gr004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/e16cc85665a9/gr005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/a7f7a14a765b/gr006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/b09f9d7b5eb1/gr007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/dc94767dfeca/gr008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/066863ba2047/gr009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/19a1/11315197/c05ca795f1ee/gr010.jpg

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