Root Square Mean Labeling of Some Graphs Obtained from Path
Rismawati Ramdani and Astrid Yuni Fanisa

Department of Mathematics
Faculty of Science and Technology
UIN Sunan Gunung Djati Bandung,

*rismawatiramdani[at]uinsgd.ac.id

Abstract

For any graph G with p vertices and q edges. A labeling f of G is said to be a root square mean labeling of G if f is a mapping of vertex set of G to integers {1,2,…,q+1} such that the induced function f* of edge e = (u,v) is defined by f*(e) =r ⌊(√(u^2 )+v^2)/2⌋ or ⌈(√(u^2 )+v^2)/2⌉ is an injection function. A graph G is called a root square mean graph if G can be labeled by a root square mean labelling. In this paper we prove that middle graph of path and disjoint union of path and the middle graph of path, are root square mean graphs.

Keywords: disjoint union, middle graph, root square mean labelling, path

Topic: Mathematics