The total domination number γt(G) is the minimum cardinality of a total dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this ...
A graph is -edge-critical, abbreviated , if its total domination number is 3 and the addition of any edge decreases the total domination number. It is known that proving the Murty-Simon Conjecture is equivalent to proving that the number of edges in a graph of order is greater than . We...
We initiate the study of signed edge majority total domination in graphs. The open neighborhood N_G(e) of an edge e in a graph G is the set consisting of all edges having a common vertex with e. Let f be a function on E(G), the edge set of G, into the set {-1, 1}. If ...
A graph is \\(3_t\\) -edge-critical, abbreviated \\(3_tEC\\) , if its total domination number is 3 and the addition of any edge decreases the total domination number. It is known that proving the Murty–Simon Conjecture is equivalent to proving that the number of edges in a \\(...
Several upper bounds are given for the maximum number of edges e possible in a graph depending upon its order p, girth g and, in certain cases, minimum degree delta. In particular, one upper bound has an asymptotic order of p1+2/(g-1) w... RD Dutton,RC Brigham - 《Graphs & Combin...
Füredi, Z.: The maximum number of edges in a minimal graph of diameter 2. J. Graph Theory 16, 81–98 (1992) MathSciNet MATH Google Scholar Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco (1979)...
The total dominator chromatic (TDC) number x_d~t(G) of G, is the minimum number of colors among all total dominator coloring of G. The neighbourhood corona of two graphs G_1 and G_2 is denoted by G_1 * G_2 and is the graph obtained by taking one copy of G_1 and | V(G_1...
If G is a graph of size m≥3 whose edges are not all incident to a single vertex, thentes(G)≤⌈m2⌉. Observe that the bound is tight for graphs where m−1 edges are incident to a single vertex and for the exceptional graph G=K5. Proof If G=(V,E) has diameter at least...
The chromatic index problem - findingthe minimum number of colours required for colouring the edges of a graph - is still unsolved for indifference graphs... CMHD Figueiredo,CPD Mello,C Ortiz - Latin American Symposium Punta Del Este 被引量: 0发表: 2000年 加载更多来源...
In this paper, we study the total dominator chromatic number of the neighbourhood of two graphs and investigate the total dominator chromatic number of r r -gluing of two graphs. Stability (bondage number) of total dominator chromatic number of G G is the minimum number of vertices (edges) ...