‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...

A graph G of order p and size q is called (a,d)-edge-antimagic total if there exists a one-to-one and onto mapping f from ∪ , ,... , such that the edge weights , ∈ form an AP progression with first term ’a’ and common difference ’d’. The graph G is said to be Super (a,d)-edge-antimagic total labeling if the , , ... , . In this paper we obtain Super (a,d)-edge-antimagic properties of certain cla...

In this paper, a complete characterization of the (super) edge-magic linear forests with two components is provided. In the process of establishing this characterization, the super edge-magic, harmonious, sequential and felicitous properties of certain 2-regular graphs are investigated , and several results on super edge-magic and felicitous labelings of unions of cycles and paths are presented...

The line graph L(G) of a graph G is defined to have as its vertices the edges of G, with two being adjacent if the corresponding edges share a vertex in G. Line graphs have a rich history. The name line graph was first used by Harary and Norman in 1960. But line graphs were the subject of investigation as far back as 1932 in a paper by H. Whitney in which he showed that for connected graphs, ed...