On The Basic Properties of Linear Graphs - I

Abstract

A linear graph is a bipartite graph with parts $\mathcal{P}$ and $\mathcal{L}$ that have propertites: LG1: Any two distinct vertices of $\mathcal{P}$ have exactly common neighbour one vertex. LG2: $\delta(G)\geq 2$. In this paper, we determined basic properties of finite linear graph.

Keywords

• common neigborhood
• linear graph
• bipartite graph

References

1. [1] A.S. Asratian, T.M.J. Denley and R. Hoggkvist, Bipartite graphs and their applications, Cambridge Uni. Press,1998, United Kingdom.
2. [2] L.M. Batten, Combinatorics of finite geometries ,Cambridge University Press, Cambridge-NewYork, 1986.
3. [3] I. Gunaltılı, A. Ulukan, and S¸. Olgun, Some Properties Of Fınıte f0,1g-Graphs , Konualp Journal Of Mathematics,1(1), 2013, 34-39.
4. [4] I. Gunaltılı, Classification Of Some f0,1g-Semigraphs, Internation Journal of Innovative Research in Computer Science & Technology,4(1),2016,10-12.
5. [5] F. Harary, D. Hsu and Z. Miller, The biparticity of a graph, J. Graph Theory 1, 1977, 131-133.
6. [6] M. Mulder,(0, l )-graph and n-cubes, Discrete mathematics 28, 1979, 179- 188.
7. [7] C. Vasudev, Combinatorics and Graph Theory, New Age Publications(Academic), India, 2007.
8. [8] D.B. West, Introduction to Graph Theory, Prentice-Hall, Englewood Clins, NJ, 1996.