Abstract

The Upper Edge Fixing Edge-to-edge Monophonic Number of a Graph

F. Merlin Sugirtha1*, P. Arul Paul Sudhahar2 and S. Robinson Chellathurai3

Scott Christian College, Nagercoil-629 003, INDIA. 2Assistant Professor, Department of Mathematics, Rani Anna Government Arts College (W), Tirunelveli-627 012, INDIA. 3Associate Professor, Department of Mathematics, Scott Christian College, Nagercoil-629 003, INDIA. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, Tamil Nadu, INDIA.

ABSTRACT

Let 𝐚 be a connected graph and 𝑒 be an edge of 𝐚. An edge fixing edge-to-edge monophonic set 𝑀(𝑒) of 𝐚 is called a minimal edge fixing edge-to-edge monophonic set of 𝑒 of 𝐚, if no proper subset of 𝑆(𝑒) is a minimal edge fixing edge-to-edge monophonic set 𝑒 of 𝐚. The maximum cardinality of a minimal edge fixing edge-to-edge monophonic set is called upper edge fixing edge-to-edge monophonic number of 𝑒 of 𝐚 and is denoted by m𝑒𝑓𝑒𝑒+(𝐚). And study some of its general properties. It is shown that, for any two positive integers a and b with 2â‰Īaâ‰Īb, there exists a connected graph 𝐚 with m𝑒𝑓𝑒𝑒(𝐚)=a and m𝑒𝑓𝑒𝑒+(𝐚)=b. AMS Subject Classification: 05C12.

Keywords :edge fixing edge-to-edge monophonic number, upper edge fixing edge-to-edge monophonic number.

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