[PDF] Top 20 Line Graphs and Quasi Total Graphs

... 3.8 Theorem: If G is a graph containing only one edge that is |EG| = 1 then the graph Q2G contains unique triangle.. is a triangle in Q2G containing the edge e..[r] ... See full document

... The quasi-total graph P(G) as the graph [9] whose vertex set is V(G)  E(G) where two vertices are adjacent if and only if (i) they are nonadjacent vertices of G or (ii) they are adjacent edges of G or ... See full document

... Ranjini et al. [10] calculated the Zagreb indices and coindices of the line graph of the subdivision graph of tadpole graph, wheel and ladder. Later Ramane et al. [9] generalized these results by finding the ... See full document

... distinguishing total chromatic number of line graph of Fan graph, double star, Friendship graph and splitting graph of path, cycle, star and sun let ...distinguishing total coloring conjecture is ... See full document

... as total domina- tion [3], equitable domination [10], fractional domination [4], global domination [9] are among mention a ...on total domination and total equitable domination in ... See full document

... x + ∈ . The question of the embedding of this graph is discussed in [4]. In that paper all isomorphism classes of finite commutative rings whose total graphs are planar or toroidal are listed. The goal of ... See full document

... subdivision graphs of the tadpole, wheel, helm and ladder graphs ...the line graphs of subdivision graphs of tadpole, wheel and ladder graphs in ...of total graph of ... See full document

... on Total graphs of Bigraphs and central graphs of cycles and paths, International Journal of Mathematics and Mathematical Sciences, Article ID 279246, 5 pages, ... See full document

... Fuzzy graph coloring is one of the most important problems of fuzzy graph theory. It uses in combinatorial optimization like traffic light control, exam-scheduling, register allocation etc. [12]. The first definition of ... See full document

... Line graphs have been studied for over seventy ...connected graphs, edge-isomorphism implies isomorphism except for K 3 and K 1,3 ...The line graph transformation is one of the most widely ... See full document

... a line graph is a function satisfying the condition that every vertex for which is adjacent to at least one vertex of for which in ...a line graph is called the Roman domination number of a graph and is ... See full document

... Labeled graphs serve as useful models for a range of applications such as coding theory, x-ray, crystallography, radar, astronomy, circuit design, channel assignments of FM radio stations and communication network ... See full document

... prove a stronger result, which is that (where denotes the line graph of ) is non-repre- sentable for . From the non-representability of we are led to a more general theorem regarding line graphs. Our ... See full document

... signed graphs (hypergraphs) and by Ψ (G ) (respectively, Ψ (H ) ) the set of all signed graphs (signed hypergraphs) whose underlying graph (underlying hypergraph) is G (respectively, H ... See full document

... perfect graphs form a subclass of absorbantly perfect graphs, and the inclusion is strict (see ...perfect graphs form a subclass of strongly Γ-perfect ... See full document

... irr(G) = ∑ ∈ ( ) |d (u) − d (v)| (1) In [6], Albertson gave some upper bounds on irregularity for trees, bipartite, and triangle-free graphs. Recall that the first Zagreb index M and the second Zagreb index M of ... See full document

... complement line domination number for some standard graphs like Cycle, Path, Complete bipartite, Wheel, Banana, Crown graph, Comb tree, Helm graph, 𝐾 𝑛 + graph, 𝐾 𝑚 ,𝑛 + graph, Book graph, Friendship graph, ... See full document

... [1] introduced notion of cordial labeling of graphs. The cocept of k-difference cordial graph was introduced in [4] . Recently Ponraj etal [5] has been introduced the concept of k-total prime cordial graph ... See full document

... The Line graph L(G) of G has the edges of G as its vertices and two vertices of L(G) are adjacent if and only if they are adjacent in ...of Line graph L(G) and also Hamiltonian-t*-laceability of Line ... See full document

... In this work, we study other important structural properties of graphs, namely planarity and outerplanarity. More precisely, we present characterizations of those trees having a planar or outerplanar 3-line ... See full document