منابع مشابه
On Graphs whose Spread is Maximal
A graph’s spread is defined as the difference between the largest eigenvalue and the least eigenvalue of the graph’s adjacency matrix. Characterizing a graph with maximal spread is still a difficult problem. If we restrict the discussion to some classes of connected graphs of a prescribed order and size, it simplifies the problem and it may allow us to solve it. Here, we discuss some results on...
متن کاملOn graphs whose maximal cliques and stable sets intersect
We say that a graph G has the CIS-property and call it a CIS-graph if every maximal clique and every maximal stable set of G intersect. By definition, G is a CIS-graph if and only if the complementary graph G is a CISgraph. Let us substitute a vertex v of a graph G′ by a graph G′′ and denote the obtained graph by G. It is also easy to see that G is a CIS-graph if and only if both G′ and G′′ are...
متن کاملEla Graphs Whose Minimal Rank Is Two
Let F be a field, G = (V, E) be an undirected graph on n vertices, and let S(F, G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For example, if G is a path, S(F, G) consists of the symmetric irreducible tridiagonal matrices. Let mr(F, G) be the minimum rank over all matrices in S(F, G). Then mr(F, G...
متن کاملGraphs whose minimal rank is two
Let F be a field, G = (V, E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For example, if G is a path, S(F,G) consists of the symmetric irreducible tridiagonal matrices. Let mr(F,G) be the minimum rank over all matrices in S(F,G). Then mr(F,G) = 1...
متن کاملOn graphs whose spectral radius
The structure of graphs whose largest eigenvalue is bounded by 3 2 √ 2 (≈ 2.1312) is investigated. In particular, such a graph can have at most one circuit, and has a natural quipu structure.
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ژورنال
عنوان ژورنال: Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics
سال: 2015
ISSN: 2217-5539
DOI: 10.5937/spsunp1502117a