# Small Components of the 5-Subgraph of a Contraction-critically 5-Connected Graph

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The set of all non-increasing non-negative integer sequences Ï€ = (d1, d2,...,dn) is denoted by NSn. A sequence Ï€ Îµ NSn is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of Ï€. The set of all graphic...

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Let $$k\ge 1$$ be an integer, and let $$G$$ be a finite and simple graph with vertex set $$V(G)$$ . A signed Roman $$k$$ -dominating function (SRkDF) on a graph $$G$$ is a function $$f:V(G)\rightarrow \{-1,1,2\}$$ satisfying the conditions that (i) $$\sum _{x\in N[v]}f(x)\ge k$$ for each vertex...

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A graph G is said to be even if all vertices of G have even degree. Given a k-edge-coloring of a graph G, for each color iâˆˆZk={0,1,â€¦,k-1} let G(i) denote the spanning subgraph of G in which the edge-set contains precisely the edges colored i. A k-edge-coloring of G is said to be an...

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Let G be a graph on n vertices and let H be a given graph. We say that G is pancyclic, if it contains cycles of all lengths from 3 up to n, and that it is H-f1-heavy, if for every induced subgraph K of G isomorphic to H and every two vertices u, v âˆˆ V ( K), dK( u, v) = 2 implies . In this...

- Invariants Concerning f -Domination in Graphs. SANMING ZHOU // Bulletin of the Malaysian Mathematical Sciences Society;2014, Vol. 37 Issue 4, p1047
Given a graph G and a function f : V(G) â†’ {0,1,2, ...}, a subset D of V(G) is called an f -dominating set of G if every vertex x outside D is adjacent to at least f (x) vertices in D. In this article we study a few graphical invariants relating to this concept.