Abstract:Let G = (V, E) be a graph. A k-coloring of a graph G is a labeling f : V (G) → T , where | T |= k and it is proper if the adjacent vertices have different labels. A graph is k-colorable if it has a proper k-coloring. The chromatic number χ(G) is the least k such that G is k-colorable. Here we study chromatic numbers in some kinds of Harary graphs.
Mathematics Subject Classification: 05C15
“…Berikut penelitian yang telah dilakukan sebelumnya terkait pewarnaan titik pada beberapa graf, yaitu pada beberapa graf harary [12], graf roda, graf kipas, graf helm, graf prisma, dan graf anti prisma [10], graf dual dari graf roda [1], korona graf kipas dengan graf kipas, graf buku segitiga dengan graf buku segitiga berorder sama [14].…”
The graph $G$ is defined as a pair of sets $(V,E)$ denoted by $G=(V,E)$, where $V$ is a non-empty vertex set and $E$ is an edge set may be empty connecting a pair of vertex. Two vertices $u$ and $v$ in the graph $G$ are said to be adjacent if $u$ and $v$ are endpoints of edge $e=uv$. The degree of a vertex $v$ on the graph $G$ is the number of vertices adjacent to the vertex $v$. In this study, the topic of graphs is vertex coloring will be studied. Coloring of a graph is giving color to the elements in the graph such that each adjacent element must have a different color. Vertex coloring in graph $G$ is assigning color to each vertex on graph $G$ such that the adjecent vertices $u$ and $v$ have different colors. The minimum number of colorings produced to color a vertex in a graph $G$ is called the vertex chromatic number in a graph $G$ denoted by $\chi(G)$.
“…Berikut penelitian yang telah dilakukan sebelumnya terkait pewarnaan titik pada beberapa graf, yaitu pada beberapa graf harary [12], graf roda, graf kipas, graf helm, graf prisma, dan graf anti prisma [10], graf dual dari graf roda [1], korona graf kipas dengan graf kipas, graf buku segitiga dengan graf buku segitiga berorder sama [14].…”
The graph $G$ is defined as a pair of sets $(V,E)$ denoted by $G=(V,E)$, where $V$ is a non-empty vertex set and $E$ is an edge set may be empty connecting a pair of vertex. Two vertices $u$ and $v$ in the graph $G$ are said to be adjacent if $u$ and $v$ are endpoints of edge $e=uv$. The degree of a vertex $v$ on the graph $G$ is the number of vertices adjacent to the vertex $v$. In this study, the topic of graphs is vertex coloring will be studied. Coloring of a graph is giving color to the elements in the graph such that each adjacent element must have a different color. Vertex coloring in graph $G$ is assigning color to each vertex on graph $G$ such that the adjecent vertices $u$ and $v$ have different colors. The minimum number of colorings produced to color a vertex in a graph $G$ is called the vertex chromatic number in a graph $G$ denoted by $\chi(G)$.
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