On partition graphs and generalizations of line graphs
نویسندگان
چکیده
منابع مشابه
On Diameter of Line Graphs
The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
متن کاملOld and new generalizations of line graphs
The line graph L(G) of a graph G is defined to have as its vertices the edges of G, with two being adjacent if the corresponding edges share a vertex in G. Line graphs have a rich history. The name line graph was first used by Harary and Norman in 1960. But line graphs were the subject of investigation as far back as 1932 in a paper by H. Whitney in which he showed that for connected graphs, ed...
متن کاملcommuting and non -commuting graphs of finit groups
فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...
15 صفحه اولD-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs
The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...
متن کاملOn an edge partition and root graphs of some classes of line graphs
The Gallai and the anti-Gallai graphs of a graph G are complementary pairs of spanning subgraphs of the line graph of G. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph G into the edge sets of the Gallai and anti-Gallai graphs of G. Based on this, an optimal algorithm to find the root graph of a line...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1977
ISSN: 0528-2195
DOI: 10.21136/cpm.1977.117959