It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G ...It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The κ-th power of G, denoted by G^κ, is the graph with vertex set V（G） in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G^3 and T（G） （the total graph of G） are ID-factor-critical, and G^4 （when ｜V（G）｜ is even） is strongly IM-extendable; if G is 2-connected, then D^2 is ID-factor-critical.展开更多
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文摘It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The κ-th power of G, denoted by G^κ, is the graph with vertex set V（G） in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G^3 and T（G） （the total graph of G） are ID-factor-critical, and G^4 （when ｜V（G）｜ is even） is strongly IM-extendable; if G is 2-connected, then D^2 is ID-factor-critical.
