Doubt m-polar subalgebras (ideals) were introduced and some properties investigated. Also, doubt positive implicative (commutative) ideals defined related results proved.

The central problem of the total-colorings is the total-coloring conjecture, which asserts that every graph of maximum degree ∆ admits a (∆+2)-total-coloring. Similar to edge-colorings—with Vizing’s edge-coloring conjecture—this bound can be decreased by 1 for plane graphs of higher maximum degree. More precisely, it is known that if ∆ ≥ 10, then every plane graph of maximum degree ∆ is (∆ + 1)...

For a simple graph G, a vertex labeling φ : V (G) → {1, 2, · · · , k} is called k-labeling. The weight of an edge xy in G, denoted by wπ(xy), is the sum of the labels of end vertices x and y, i.e. wφ(xy) = φ(x) + φ(y). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two different edges e and f , there is wφ(e) 6= wφ(f). The minimum k for which the g...

A procedure for counting edge covers of simple graphs is presented. The procedure splits simple graphs into non-intersecting cycle graphs. This is the first “low exponential” exact algorithm to count edge covers for simple graphs whose upper bound in the worst case is O(1.465575 × (m + n)), where m and n are the number of edges and nodes of the input graph, respectively.

Let G = (V,E) be a finite undirected graph without loops and multiple edges. A subset M ⊆ E of edges is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of M . In particular, this means that M is an induced matching, and every edge not in M shares exactly one vertex with an edge in M . Clearly, not every graph has a d.i.m. The Dominating Induced ...

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

The research of Boolean index sets of graphs is one of the important graph theory in the graph theory. Boolean index sets of graphs are to use the vertex sets and the edge sets of graphs to study the characteristics of various graphs and their inherent characteristics through corresponding the mapping function to 2 Z . Its theory can be applied to information engineering, communication networks...