On total matching numbers and total covering numbers of complementary graphs
نویسندگان
چکیده
منابع مشابه
On total matching numbers and total covering numbers of complementary graphs
Let G be a graph with edge set E and vertex set V. A vertex u is said to cover itself, all edges incident with u and all vertices joined to u . An edge (u, v) covers itself, the vertices u and v and all edges incident with u or v . Two elements of E U V are independent if neither covers the other . A Subset ~', of elements of E U V is called a total cover if the elements of W cover G and W is m...
متن کاملTotal $k$-Rainbow domination numbers in graphs
Let $kgeq 1$ be an integer, and let $G$ be a graph. A {it$k$-rainbow dominating function} (or a {it $k$-RDF}) of $G$ is afunction $f$ from the vertex set $V(G)$ to the family of all subsetsof ${1,2,ldots ,k}$ such that for every $vin V(G)$ with$f(v)=emptyset $, the condition $bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}$ is fulfilled, where $N_{G}(v)$ isthe open neighborhood of $v$. The {it weight} o...
متن کاملTotal Domination and Matching Numbers in Claw-Free Graphs
A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. The matching number of G is the maximum cardinality of a matching of G. A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. If G does not contain K1,...
متن کاملOn (d, 1)-total numbers of graphs
A (d, 1)-total labelling of a graph G assigns integers to the vertices and edges of G such that adjacent vertices receive distinct labels, adjacent edges receive distinct labels, and a vertex and its incident edges receive labels that differ in absolute value by at least d. The span of a (d, 1)-total labelling is the maximum difference between two labels. The (d, 1)-total number, denoted λTd (G...
متن کاملOn the total graph of Mycielski graphs, central graphs and their covering numbers
The technique of counting cliques in networks is a natural problem. In this paper, we develop certain results on counting of triangles for the total graph of the Mycielski graph or central graph of star as well as completegraph families. Moreover, we discuss the upper bounds for the number of triangles in the Mycielski and other well known transformations of graphs. Finally, it is shown that th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1977
ISSN: 0012-365X
DOI: 10.1016/0012-365x(77)90102-9