A Characterization of Circle Graphs in Terms of Multimatroid Representations

The isotropic matroid $M[IAS(G)]$ of a looped simple graph $G$ is a binary matroid equivalent to the isotropic system of $G$. In general, $M[IAS(G)]$ is not regular, so it cannot be represented over fields of characteristic $\neq 2$. The ground set of $M[IAS(G)]$ is denoted $W(G)$; it is partitioned into 3-element subsets corresponding to the vertices of $G$. When the rank function of $M[IAS(G)]$ is restricted to subtransversals of this partition, the resulting structure is a multimatroid denoted $\mathcal{Z}_{3}(G)$. In this paper we prove that $G$ is a circle graph if and only if for every field $\mathbb{F}$, there is an $\mathbb{F}$-representable matroid with ground set $W(G)$, which defines $\mathcal{Z}_{3}(G)$ by restriction. We connect this characterization with several other circle graph characterizations that have appeared in the literature.

GRACEFUL LABEING AND RHO TOPI LABELING ON THE 8-BINTANG GRAPH WITH C3 FOR N ODD

<p><em>This paper we propose graceful labeling and </em> <em> </em><em>labeling on a graph then referred to as 8-Bintang graph, the basic idea of formulation graceful labeling and </em> <em> </em><em>labeling on an alfabet bintang graphs wih the question a stars graph </em> <em>.</em><em> Then we constructing graceful labeling and </em> <em> </em><em>labeling</em><em> </em><em>on the 8-Bintang graph with circle graph </em> <em> for </em> <em> odd. The results obtained are illustrated in the theorem that the 8-Bintang graph </em><em>with</em><em> </em> <em> for </em> <em> odd has the following </em><em>graceful labeling with the proof.</em><em></em></p>

IMPLEMENTASI ALGORITMA MODIFIKASI BROYDEN-FLETCHER-GOLDFARB-SHANNO (MBFGS)

The concept of minimum resolving set has proved to be useful and or related to a variety of fields such as Chemistry, Robotic Navigation, and Combinatorial Search and Optimization. Two graph are path graph (𝑃𝑛) anf circle graph (𝐶𝑚). The corona product 𝑃𝑛 ⨀𝐶𝑚 is defined as the graph obtained from 𝑃𝑛and 𝐶𝑚 by taking one copi of 𝑃𝑛 and 𝑚1copies of 𝐶𝑚 and joining by an edge each vertex from the 𝑛𝑡ℎ copy of 𝑃𝑛 with the 𝑚𝑡ℎ vertex of 𝐶𝑚. 𝑃𝑛 ⨀ 𝐶𝑚 and 𝐶𝑚⨀𝑃𝑛 not commute to 𝑛≠𝑚, it is showed that order of graph 𝑃𝑛 ⨀ 𝐶𝑚 different with graph 𝐶𝑚⨀𝑃𝑛. Based on research obtained 𝑑𝑖𝑚(𝑃𝑛⨀𝐶𝑚)=𝑛.𝑑𝑖𝑚(𝑊1,𝑚) dan 𝑑𝑖𝑚(𝐶𝑚⨀𝑃𝑛)=𝑚.𝑑𝑖𝑚 (𝐾1+𝑃𝑛)Keyword : Resolving Sets, Metric Dimension, Path Graph, Circle Graph, Corona Graph

Isotropic Matroids II: Circle Graphs

We present several characterizations of circle graphs, which follow from Bouchet’s circle graph obstructions theorem.