Let G be a graph of order n and maximum degree ∆(G) and let γt (G) denote the minimum cardinality of a total dominating set of a graph G. A graph G with no isolated vertex is the total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G − v is less than the total domination number of G. We call these graphs γt -cri...

The clique graph of G, K(G), is the intersection graph of the family of cliques (maximal complete sets) of G. Clique-critical graphs were defined as those whose clique graph changes whenever a vertex is removed. We prove that if G has m edges then any clique-critical graph in K−1(G) has at most 2m vertices, which solves a question posed by Escalante and Toft [On clique-critical graphs, J. Combi...

This is a replacement paper. Some of the conclusions from statistical graph theory are reiterated in the sixth section, but not fully resolved therein. Most of the redundancies in the later sections have been deleted. An important number-theoretical technique in the opening section relates to one of the main techniques in the last (sixth) section.

The smallest number of edges that have to be deleted from a graph to obtain a bipartite spanning subgraph is called the bipartite edge frustration of G and denoted by φ(G). In this paper we determine the bipartite edge frustration of some classes of composite graphs. © 2010 Elsevier B.V. All rights reserved.

A graph G with maximum degree and edge chromatic number ′(G)> is edge-critical if ′(G− e)= for every edge e of G. New lower bounds are given for the average degree of an edge-critical graph, which improve on the best bounds previously known for most values of . Examples of edge-critical graphs are also given. In almost all cases, there remains a large gap between the best lower bound known and ...

A graph is called γ -critical if the removal of any vertex from the graph decreases the dominationnumber,while a graphwith no isolated vertex isγt -critical if the removal of any vertex that is not adjacent to a vertex of degree 1 decreases the total domination number. A γt -critical graph that has total domination number k, is called k-γt -critical. In this paper, we introduce a class of k-γt ...

For natural numbers k and n, where 2 ≤ k ≤ n, the vertices of a graph are labeled using the elements of the k-fold Cartesian product In× In×· · ·× In. Two particular graph constructions will be given and the graphs so constructed are called generalized matrix graphs. Properties of generalized matrix graphs are determined and their application to completely independent critical cliques is invest...

This paper deals the graphs for which the removal of any edge changes the majority domination number of the graph. γM -critical edges, γM -redundant edges, γM -durable graphs and γM -critical graphs are studied. Further, majority domination critical edges and majority domination critical graphs are characterized.

The Stac3 gene is exclusively expressed in skeletal muscle, and Stac3 knockout is perinatal lethal in mice. Previous data from Stac3-deleted diaphragms indicated that Stac3-deleted skeletal muscle could not contract because of defective excitation-contraction (EC) coupling. In this study, we determined the contractility of Stac3-deleted hindlimb muscle. In response to frequent electrostimulatio...