Abstract
<p><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">In this paper, we prove Heronian Mean labeling of some degree splitting graphs. Already we have proved Heronian Mean labeling for some standard graphs. Here we prove that degree splitting of Path <span lang="EN-US">P<sub>3</sub></span></span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">, Path <span lang="EN-US">P<sub>4</sub></span>, <span lang="EN-US">P<sub>3</sub>ʘK<sub>1</sub></span></span></span><span lang="EN-US"><span><span style="font-family: 宋体; font-size: medium;">, <span lang="EN-US">P<sub>2</sub>ʘK<sub>1,2</sub></span>, <span lang="EN-US">P<sub>2</sub>ʘK<sub>1,3</sub></span>, <span><span><sub> </sub></span></span><span lang="EN-US">P<sub>2</sub>ʘK<sub>3</sub></span> </span></span><span style="font-family: 宋体; font-size: medium;">are Heronian Mean graphs.</span></span></p>
Highlights
By a graph we mean a finite undirected graph without loops or parallel edges
We prove Heronian Mean labeling of some degree splitting graphs
Already we have proved Heronian Mean labeling for some standard graphs
Summary
By a graph we mean a finite undirected graph without loops or parallel edges. For all detailed survey of graph labeling, we refer to J. The concept of Mean labeling was introduced in (Somasundaram & Ponraj, 2003). The concept of Harmonic Mean labeling was introduced in (Somasundaram, Ponraj, & Sandhya). The concept of Harmonic Mean labeling on Degree Splitting graph was introduced in (Sandhya, Jeyasekharan, & David). Motivated by the above results and by the motivation of the authors we study the Heronian Mean labeling on Degree Splitting graphs. Heronian Mean labeling was introduced in (Sandhya, Merly, & Deepa) and the Heronian Mean labeling of some standard graphs was proved in (Sandhya, Merly, & Deepa). A graph G=(V,E) with p vertices and q edges is said to be a Heronian Mean graph if it is possible to label the vertices x V with distinct labels f(x) from 1,2,...,q+1 in such a way that when each edge e = uv is labeled with, f(e. In this case f is called a Heronian Mean labeling of G. The graph G and its degree splitting graph DS(G) are given in figure:
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
