The nullity of a graph G is the multiplicity zero as an eigenvalue its adjacency matrix. An assignment weights to vertices graph, that satisfies sum condition over neighbors each vertex, and uses maximum number independent variables denoted by high weighting graph. This applicable tool used determine Two types graphs are defined, change their nullities studied, namely, G+ab constructed from add...

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Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For each graph G, there is an associated minimum rank class, M R (G) consisting of all matrices A ∈ S (G) with rankA = mr (G), the minimum rank among all matrices in S (G)....

We implemented support for non-null types in Java according to the description in [1]. We built our implementation on top of the Polyglot Java compiler as a language extension. Our extension allows programmers to provide annotations specifying whether a variable is allowed to ever take on a null value and provides an augmented type system to enforce these guarantees. Once the separation between...

Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For each graph G, there is an associated minimum rank class, M R (G) consisting of all matrices A ∈ S (G) with rankA = mr (G), the minimum rank among all matrices in S (G)....

Let A and id="M2"> mathvariant="script">B be two closed linear relations acting between Banach spaces id="M3"> X id="M4"> Y , let id="M5"> λ a complex number. We study the stability of nullity deficiency id="M6"> when it is perturbed by id="M7"> . In particular, we sho...