New Results on Face Magic Mean Labeling of Graphs

Abstract

In the midst of the 1960s, a theory by Kotzig-Ringel and a study by Rosa sparked curiosity in graph labeling. Our primary objective is to examine some types of graphs which admit Face Magic Mean Labeling (FMML). A bijection <img src=image/13429259_01.gif> is called a (1,0,0) F-Face magic mean labeling [FMML] of <img src=image/13429259_02.gif> if the induced face labeling <img src=image/13429259_03.gif> <img src=image/13429259_04.gif> A bijection <img src=image/13429259_05.gif> is called a (1,1,0) F-Face magic mean labeling [FMML] of <img src=image/13429259_02.gif> if the induced face labeling <img src=image/13429259_06.gif> <img src=image/13429259_07.gif> In this paper it is being investigated that the (1, 0, 0) – Face Magic Mean Labeling (F-FMML) of Ladder graphs, Tortoise graph and Middle graph of a path graph. Also (1,0,0) and (1,1,0) F-Face Magic Mean Labeling is verified for Ortho Chain Square Cactus graph, Para Chain Square Cactus graph and some snake related graphs like Triangular snake graphs and Quadrilateral snake graphs. For a wide range of applications, including the creation of good kind of codes, synch-set codes, missile guidance codes and convolutional codes with optimal auto correlation characteristics, labeled graphs serve as valuable mathematical models. They aid in the ability to develop the most efficient non-standard integer encodings; labeled graphs have also been used to identify ambiguities in the access protocol of communication networks; data base management to identify the best circuit layouts, etc.