منابع مشابه
Sudoku Graphs are Integral
Sudoku graphs have only 5 or 6 distinct eigenvalues and all of them are integers. Moreover, the associated eigenspaces admit bases with entries from the set {0, 1,−1}.
متن کاملWhich Cayley Graphs are Integral?
Let G be a non-trivial group, S ⊆ G \ {1} and S = S−1 := {s−1 | s ∈ S}. The Cayley graph of G denoted by Γ(S : G) is a graph with vertex set G and two vertices a and b are adjacent if ab−1 ∈ S. A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine all connected cubic integral Cayley graphs. We also introduce some infinite families of connected integra...
متن کاملCritical Sets for Sudoku and General Graphs
We discuss the problem of finding critical sets in graphs, a concept which has appeared in a number of guises in the combinatorics and graph theory literature. The case of the Sudoku graph receives particular attention, because critical sets correspond to minimal fair puzzles. We define four parameters associated with the sizes of extremal critical sets and (a) prove several general results abo...
متن کاملMatching Integral Graphs of Small Order
In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...
متن کاملGroups all of whose undirected Cayley graphs are integral
Let G be a finite group, S ⊆ G \ {1} be a set such that if a ∈ S, then a−1 ∈ S, where 1 denotes the identity element of G. The undirected Cayley graph Cay(G, S) ofG over the set S is the graphwhose vertex set is G and two vertices a and b are adjacent whenever ab−1 ∈ S. The adjacency spectrum of a graph is the multiset of all eigenvalues of the adjacency matrix of the graph. A graph is called i...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/263