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Abstract Given a graph G, the mixed graph D G is obtained from G by orienting some of its edges, where G is called the underlying graph of D G… Click to show full abstract
Abstract Given a graph G, the mixed graph D G is obtained from G by orienting some of its edges, where G is called the underlying graph of D G . Let p ( D G ) , n ( D G ) (resp. p ( G ) , n ( G ) ) be the positive inertia index and negative inertia index of D G (resp. G). In this paper, we first establish the inequalities − d ( G ) ⩽ p ( D G ) − p ( G ) ⩽ d ( G ) and − d ( G ) ⩽ n ( D G ) − n ( G ) ⩽ d ( G ) , where d ( G ) is the dimension of cycle space of G. Furthermore, all the corresponding extremal graphs are characterized.
Keywords:
mixed graph;
indices mixed;
underlying graph;
graph;
inertia indices;
relations inertia
Journal Title: Linear Algebra and its Applications
Year Published: 2020
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Journal Title: Linear Algebra and its Applications
Year Published: 2020
Link to full text (if available)
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recommendations!