2021•arXiv (Cornell University)Open access
The transformation of edge-regular and pseudo strongly regular graphs\n under graph operations
Jeepamol J. Palathingal, Aparna Lakshmanan S, Greg Markowsky
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Abstract
The graph $G$ is said to be strongly regular with parameters\n$(n,k,\\lambda,\\mu)$ if the following conditions hold:\n (1) each vertex has $k$ neighbours; (2) any two adjacent vertices of $G$ have\n$\\lambda$ common neighbours; (3) any two non-adjacent vertices of $G$ have\n$\\mu$ common neighbours.\n In this paper we study two weaker notions of strongly regular graphs. A graph\nsatisfying the conditions $(1)$ and $(2)$ is called an edge-regular graph with\nparameters $(n,k,\\lambda)$. We call a graph satisfying the conditions $(1)$ and\n$(3)$ a pseudo strongly regular graph with parameters $(n,k,\\mu)$. In this\npaper we study the impact of various graph operations on edge regular graphs\nand pseudo strongly regular graphs.\n
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