Minimum Total Irregularity of Totally Segregated ∞-Bicyclic Graph
T. F. Jorry1, K. S. Parvathy2

1T. F. Jorry, Assistant Professor, Department of Mathematics, Mercy College, Palakkad (Kerala), India.
2K. S. Parvathy, Associate Professor, Department of Mathematics, St. Mary’s College, Thrissur (Kerala), India.
Manuscript received on 26 March 2019 | Revised Manuscript received on 05 April 2019 | Manuscript Published on 27 April 2019 | PP: 660-663 | Volume-7 Issue-6S2 April 2019 | Retrieval Number: F10790476S219/2019©BEIESP
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Abstract: A bicyclic graph is a simple connected graph in which the number of edges equals the number of vertices plus one. A bicyclic graph, in which any two adjacent vertices have distinct degrees, is a totally segregated bicyclic graph. Total Irregularity of a graph is defined as: irrt(G)=𝟏 𝟐 𝒖,𝒗∈𝑽(𝑮) |𝒅𝑮 𝒖 − 𝒅𝑮𝒗|. In this paper, total irregularity of totally segregated ∞- bicyclic graph is discussed and some properties of totally segregated ∞- bicyclic graph G with ∆=4 and n4(G)=1 is found. The basic bicycle denoted by∞(p,q,1) is obtained from two vertexdisjoint cycles CpandCq by identifying one vertex of Cp and one vertex of Cq. The ∞-bicyclic graph is obtained by attaching some trees to basic bicycle ∞(p,q,1). In this paper we determine the minimum total irregularity of totally segregated ∞- bicyclic graph on n vertices. Degree sequence of totally segregated ∞-bicyclic graph with minimum total irregularity is also found.
Keywords: Total Irregularity, Totally Segregated ∞-Bicyclic Graph, Basic Bicycle ∞(p,q,1), Degree Sequence.
Scope of the Article: Cryptography and Applied Mathematics