TAILIEUCHUNG - Necessary and sufficient conditions for quasi-strong regularity of graph product

A k-regular graph (k ≥ 1) with n vertices is called a quasi-strongly regular graph with parameter λ (λ ∈ N) if any two adjacent vertices have exactly λ neighbors in common. A graph product is a binary operation on graphs. It is useful to describe graph as product of other primitive graphs. In this paper we present some necessary and sufficient conditions for Decartes product, Tensor product, Lexicographical product and Strong product to be quasi-strongly regular. | Journal of Computer Science and Cybernetics, , (2018), 161–169 DOI NECESSARY AND SUFFICIENT CONDITIONS FOR QUASI-STRONG REGULARITY OF GRAPH PRODUCT TUAN DO MINH1 , HOA VU DINH2 1 Nam Dinh Teacher Training College, PhD Student in Ha Noi University of Science, VNU 2 Hanoi University of Education; 2 hoavd@ Abstract. A k -regular graph (k ≥ 1) with n vertices is called a quasi-strongly regular graph with parameter λ (λ ∈ N) if any two adjacent vertices have exactly λ neighbors in common. A graph product is a binary operation on graphs. It is useful to describe graph as product of other primitive graphs. In this paper we present some necessary and sufficient conditions for Decartes product, Tensor product, Lexicographical product and Strong product to be quasi-strongly regular. Keywords. Quasi-strongly regular graph, product graph. 1. INTRODUCTION We consider in this paper only undirected and simple graphs. Let G = (V, E) be a graph with the vertices set V and the edges set E. The neighborhood of a vertex v ∈ V , the set of adjacent vertices of v, is denoted by N (v). If two vertices i and j are adjacent, then we write i ∼ j. A quasi-strongly regular graph with parameters (n, k, λ) [8], denoted by qsrg(n, k, λ), is a k-regular graph on n vertices satisfying the condition: if i ∼ j then λ =

• Toán học
• Journal of Computer Science and Cybernetics
• Necessary and sufficient conditions
• Quasi strong regularity of graph product
• Quasi strongly regular graph
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