2 research outputs found
Integer k-matching preclusion of graphs
As a generalization of matching preclusion number of a graph, we provide the
(strong) integer -matching preclusion number, abbreviated as number
( number), which is the minimum number of edges (vertices and edges)
whose deletion results in a graph that has neither perfect integer -matching
nor almost perfect integer -matching. In this paper, we show that when
is even, the () number is equal to the (strong) fractional
matching preclusion number. We obtain a necessary condition of graphs with an
almost-perfect integer -matching and a relational expression between the
matching number and the integer -matching number of bipartite graphs. Thus
the number and the number of complete graphs, bipartite
graphs and arrangement graphs are obtained, respectively.Comment: 18 pages, 5 figure
Construction for the Sequences of Q-Borderenergetic Graphs
This research intends to construct a signless Laplacian spectrum of the complement of any k-regular graph G with order n. Through application of the join of two arbitrary graphs, a new class of Q-borderenergetic graphs is determined with proof. As indicated in the research, with a regular Q-borderenergetic graph, sequences of regular Q-borderenergetic graphs can be constructed. The procedures for such a construction are determined and demonstrated. Significantly, all the possible regular Q-borderenergetic graphs of order 7<n≤10 are determined